Beat Frequencies: Newsletter Challenge (01/22/08)

A physics professor stated to his class that a live performance of an orchestral piece will always sound different from a high-quality Hi-Fi reproduction. He claims this is because in the live performance, the listener will be able to hear some beat frequencies between some higher frequency harmonics (above the hearing range), whereas in the recorded reproduction (unable to record the original, high harmonics), the beat frequencies will not exist. A student said, "Nonsense!" Is the student correct?

IMHO, not being an acoustics engineer, but using some common sense (I hope), in theory, it sounds like the professor could be right, but I think he is incorrect. Let's see, did I equivocate enough? <grin>

Seriously, though, since beat frequencies are the difference between two frequencies that are very close (whenever you mix frequencies your products include both the sum of the original frequencies and their difference). If a human can normally hear up to about 20 kHz, and there are harmonics over that, their difference could easily be back down in the audible range. Say two slightly unmatched string instruments played a note which had harmonic tones at 25,000 Hz and 25,200 Hz, the beat frequency would be 200 Hz, which would be at the low end of frequencies detectable by humans.

However, in practice, the amplitude of these harmonics, as well as their beat frequencies, would be so low, and covered up by so many other tones, they would be undetectable by a human ear. So in this sense the student is correct. But also, the student is correct because any beat frequencies that fell into the human audible range and could be heard in the concert setting, should also be recorded by the "Hi-Fi" apparatus.

There would, of course be noticeable differences between a live performance and a "high-quality Hi-Fi reproduction", since it is almost impossible to reproduce the same acoustical "presence" of a concert hall in a different listening venue, although many electronics manufacturers are getting better and better with various "equalization" methods and other electronic and digital wizardry. However, I doubt that any of the difference could be ascribed to the theory advocated by the professor.

Of course, I could be wrong, since I am only an engineer. I am sure I will be corrected by my betters.

Wait!

Let's take an example. Let's assume we can hear up to 25 kHz (I can't and nobody else can), but let's assume that we can. A beat between two competing tones of 25 kHz and 25.01 Khz will produce a beat of 10 Hz.

However, that sound is manifested as a combination of the two competing tones. The result is a modulated tone, not a 10Hz tone, 25 kHz tone, and a 25.01 kHz tone. You hear a single note that warbles at 10 Hz. When you superimpose the two tones' upon each other you get areas where the resulting tone is amplified and nullified depending on the antinodes and nodes of the combination of the two tones. This is what the beat actually is. It is a modulated fundamental note based on a 25 kHz note and a 25.01 kHz note.

You can have the best HiFi system in the world and then listen live. Neither scenario will be heard in reality. First, HiFi recording filters frequencies above 20 kHz to avoid the Niquest point for a CD recording, which samples at 44.1 kHz. Almost no one can hear above 20 kHz in a live setting or in a living room.

Point is, you can't hear the beat frequencies because the ultrasonics that the professor insists produce beat frequencies is in itself inaudible. You can't hear competing ultrasonics warble.

My first point drooled on about the energy levels of the beat frequencies. Again, even if the beat frequency was 800 Hz, the energy of the 800 Hz beat is so small that it is lost in background noise and inaudible.

Point is, you can't hear the beat frequencies because the ultrasonics that the professor insists produce beat frequencies is in itself inaudible. You can't hear competing ultrasonics warble.

Exactly. In my slightly earlier posts I put up a link to a double tone generator. If the tones are inaudible, the beat is also inaudible (despite the fact that the amplitude of the envelope of the combined frequencies is double that of the two contributing frequencies). To hear the envelope frequency, one would need a rectifier.

Please don't overstate the case: actual signal at difference frequencies will be generated by almost anything non-linear - be it eardrum, hair-cell, or anything in between.

Even air can produce non-linear distortion - it is reasonably well-known that this effect can be quite a significant limitation on the amplitudes that horn loudspeakers can handle.

Obviously, for most forms of non-linearity (ideal rectification being one of the exceptions) the level of the difference frequency rises more rapidly than the levels of the generating signals. And such evidence as exists indicates that the effects of ultrasonic components are most significant at high sound levels. So this could be a contributor to lack of realism. [But, as I said elsewhere, the professor is still wrong]

Fyz

A trigonometric reminder:
[cos(a) + cos(b)]² = cos²(a) + cos²(b) + 2.cos(a).cos(b) = cos(2.a)/2 + cos(2.b)/2 - 1 + cos(a+b)/2 + cos(a-b)/2

The student is correct. The reason a live performance is percieved as different from a reproduction is due to the limitations of the recording process. Between recording the live sound through sensors (microphones), processing, transferring audio to a medium (CD or 8 track for you old guys); the original sound loses something. Despite the high quality of recording equipment, it cannot truely reproduce the broadband audio spectrum without inserting some noise and frequency distortion.

Digital recording has its own issues with regard to sampling rates, etc... But we can save that for another challenge.

While I agree with your assertion about the difficulty of reproduction without adding noise and frequency distortion (as well as digital sampling errors), I think there is more to this question than just that. See my answer in #1 above.

No. I did do a "Wait!" followup before reading your reply, but it just elaborates on your point.

As Jorrie pointed out, reproduction of sound always looses something, be it dynamic range, distortion, frequency, or tone color. Not to mention room acoustics where it is played back and there are more senses than your ears at work in a live recording. Your whole emotional psyche is different, too, so you perceive things differently.

I think we should argue the merits of wire! ;-)

Theory says yes. Typical recordings cap the frequency range upper and lower limits with steep roll off filters. The upper limit is typically going to be about 20 kHz.

However, higher frequencies have a much lower displacement of air than lower frequencies. Beat frequencies between high frequency sounds will consequently have a much lower amplitude when generated from high frequencies.

For a note at 100 Hz to have the same acoustic volume level as a note at 1 kHz (assuming the listener has normal ears) the 100 Hz transducer must displace more volume of air.

What I am trying to say is the high frequency notes above 20 kHz will have very, very low volume displacement of air. Any beat frequency will have a subsequently lower volume of displacement and be rendered virtually inaudible.

I think the next challenge question should be on the quality of speaker wire and AC cords such as the $1500 Kaptivator!!! A.K.A. Copper Snake Oil.

Good point AH. I think that complements (not compliments) my argument in #1 quite nicely. Do you see anything in my argument that is not correct?

Oops, see post #9. I hit the wrong reply! ;-)

I think the next challenge question should be on the quality of speaker wire and AC cords such as the $1500 Kaptivator!!! A.K.A. Copper Snake Oil.

This is absolutely amazing! I read through the link chuckling, thinking someone with a dry sense of humor had put it together. But then I went to the JPS Site, and they appear to be serious!!! $1499 for a power cord.

The Kaptovator was made using no inductive or capacitive devices and uses no shielding elements that Skubinski feels would limit the uninterrupted and speedy flow of power to its destination. The Optimized Field Matrix designation on the Kaptovator's clear sleeve indicates that it was designed to be non-reactive to a wide variety of components and applications.

"No inductive or capacitive devices"... other than the wire, the insulator and the wire spacing. The uninterrupted and speedy flow of power??? AC power is notoriously noisy, variable, etc. This cord, by their own admission, does nothing to the power to condition it, has no shielding, and conducts all the garbage in your house lines directly to your amplifier. (With which any good power supply is perfectly able to contend.) You've got 100' of cheap wire leading to your wall outlet, which is fed by miles of power lines... and replacing the last 6' with ordinary wire is supposed to change something?

Break in time??!! Are the electrons polishing their pathways? Anyone who would pay $1499 for one of these truly deserves to do so.

I have amused myself thinking of all sorts of outlandish things people might pay money for -- but I don't think I've ever come up with anything to top this.

Yep, there's one born every minute.

-------------------------SNIP---------------------

Kapton is a high-tech, golden-colored dielectric used mainly in space and military applications. Using air as a reference (which is what all insulators are measured against), JPS set out to find the optimum dielectric to safely insulate the cord. They found Kapton to be a great insulator but also a very expensive one, hence the high price.

-------------------------SNIP-----------------------

used mainly in space and military applications.......Oh and general manufacturing.

but also a very expensive one........ Unless you buy it with glue on apparently:

From Kaptontape.com

Tapes for electronic automotive and general manufacturing.

KPT5-1/4 1/4" x 36 yds roll $31.98

Don't get me started on silver speaker cables.

BTW I've been playing with the dual tone generator you posted the link to, on two separate computers. I'm still convinced that our ears can't de-modulate the higher frequencies. But, I did notice that, although I thought I couldn't hear say 16000 Hz on its own I could hear 16000 mixed with 16001 and could subsequently hear the 16000 on its own if I kept turning the generator on and off. I also noticed that some crappy headphones produced audible sounds when driven with a pure 20K tone.

"I also noticed that some crappy headphones produced audible sounds when driven with a pure 20K tone." Would that be random noise (check any joints?) or subharmonic generation (possible, but requires very specific fortuitous resonances**)?

Either way, those 'phones must be exceedingly crappy (great technical term)!

**Unfortunately, I couldn't find a simple downloadable reference

"used mainly in space and military applications.......Oh and general manufacturing.

but also a very expensive one........ Unless you buy it with glue on apparently:

From Kaptontape.com

Tapes for electronic automotive and general manufacturing.

KPT5-1/4 1/4" x 36 yds roll $31.98

Don't get me started on silver speaker cables."

Well, well. "Expensive" is a relative term, now isn't it? Relative to a standard roll of vinyl electrical tape, about a buck or so, your $32 dollar roll of Kapton IS pretty expensive. And, yes, when first developed, as in many new engineering materials, Kapton WAS used mainly in space and military applications, where price is only a secondary, or tertiary consideration. As its capabilities became more well known and production volumes increased it became more affordable, finding many new applications in automotive, electronics, and other industries.

Silver (plated? I can't imagine they are made of solid silver!) speaker cables may not be "worth their weight in gold", but for an audiophile with more money that sense, they may be seen as desirable. There are some good qualities about silver cables that make them better than plain copper. When copper oxidizes, its oxide is non-conductive, making some connections highly resistive, diminishing the power handling capability of the cable. Whereas, silver oxide is conductive. That is why you find silver-plated connectors in many laboratory instruments and radio frequency (RF) components. Are silver cables worth the extra money? If your cables are exposed to weather and you value reliability very highly, then they might be. But most consumers would not notice the difference between ordinary copper cables and silver ones.

I think the student is right that the prof was waffling, but then, the sound from a Hi-Fi can never ever equal the sound from a live performance! The issue is not beat frequencies from the high end because, as STL said, the beat frequencies will be recorded in any case. The issue is that however many microphones and loudspeakers you deploy, the acoustics of the concert hall can never be replicated.

Jorrie

Jorrie:

If you recall the related "Audio Spotlight" detection controversy that Moose introduced, I believe we have a new concurring vote in comment #7. That would seem to indicate an opinion that non-linear elements in the ear allow us to perceive beat frequencies between ultrasonic "sounds". No one seems to be claiming that the non-linearity of air is responsible.

DickL

Ultrasonic nonlinearity would be observed only at high sound levels - but still nowhere near the levels required for non-linearity in the air. I believe that non-linear methods have been proposed to produce virtual sound sources in mid-air using so-called hypersonic sources; if so, this would almost certainly use a focussed sound beam to activate a relatively small volume - using higher frequencies presumably allows a smaller focus; I imagine it would be quite difficult to achieve fidelity using such methods.

Regarding non-linearity generation in hair-cells etc - I assume both frequencies would need to be near resonances of the hair-cells - which (I again assume) would be at considerably more than there-times the detected frequency, and unlikely to correspond to harmonic frequencies of the fundamental frequency of the hair-cell. The consequent information-processing paths would therefore either simply detect presence of unrelated frequency pulses at the correctly related levels, or be based on expected frequency relationships (unbelievably complex??)

Hi DL, you wrote:

"That would seem to indicate an opinion that non-linear elements in the ear allow us to perceive beat frequencies between ultrasonic "sounds"."

I don't think the Hi-Fi sound vs. live sound issue is in any way connected to that ultra-sound issue that you mentioned. If I remember correctly, those were very high frequencies, as Fyz has mentioned and not harmonics that an orchestra could possible produce. Some demodulation in the non-linear air was involved, which I don't think happens in this scenario.

Jorrie

Dont forget-the beat frequencies in an orchestral piece are being created by many different and/or multiple species. i.e. the first vs. second violins, or the violins vs. the French Horns. When it is reproduced on speakers, its almost impossible to get beat frequencies from one component-as in the woofers cannot vibrate in two waveforms at the same time efficiently as to create a beat. To prove this I could reproduce when I was trying to play some Van Halen on my brothers guitar when I was 17, and greated a strong enough feedback loop to blow his speakers.

"The issue is that however many microphones and loudspeakers you deploy, the acoustics of the concert hall can never be replicated."

I think that's quite relevant the fact that the microphones are not placed in the same position as the listener's ears in the concert hall so they're picking the sound, in the best case, as is modified by the concert hall acoustics in the position where they are placed. If you move around in your listening room you'll find quite relevant differences in sounds in different positions due to nodes of stationary waves.

Having such a record you'll need a listening room such that the position of the speakers (let's imagine perfect reproduction chain w/o any type of loss or dynamic limits) combined with the room geometry, forniture and materials provides you with the same dynamic response you get from the instruments in the given concert hall's listening position while the hall is filled with people (whose dampening effect on stationary waves is not easy to dismiss).

Likely most of the times the microphones are made and arranged so that as little as possible of the noises coming from the concert audience is captured and the registration and reproduction chain are not perfect, hence with real world records there is no hope to really reproduce the live event.

Anyone that has listened to live non-amplified music knows by direct experience what the professor said.

This post by Jorrie (below) is to me the clearly obvious response. Thank you for getting it out there. Add the early reflections and reverberations from every surface in the room and the spatial relationships of each musician and even the interference of each musician, their instruments, their clothing, the percentage of humidity in the air and any comments regarding speakers & Hi Fi are simply ludicrous. For instance, you cannot record a clarinet with any realism. The sound eminates from each uncovered hole as well as the bell. Where would you mike it from, an anechoic chamber with one microphone? At what distance? Would you do better with thirty mikes, what about phase cancellation? Maybe look up some info on early biaural recording techniques, you will get a taste of what this all really means.

Whitaker

"The issue is that however many microphones and loudspeakers you deploy, the acoustics of the concert hall can never be replicated."

I think that's quite relevant the fact that the microphones are not placed in the same position as the listener's ears in the concert hall so they're picking the sound, in the best case, as is modified by the concert hall acoustics in the position where they are placed. If you move around in your listening room you'll find quite relevant differences in sounds in different positions due to nodes of stationary waves.

Having such a record you'll need a listening room such that the position of the speakers (let's imagine perfect reproduction chain w/o any type of loss or dynamic limits) combined with the room geometry, forniture and materials provides you with the same dynamic response you get from the instruments in the given concert hall's listening position while the hall is filled with people (whose dampening effect on stationary waves is not easy to dismiss).

Likely most of the times the microphones are made and arranged so that as little as possible of the noises coming from the concert audience is captured and the registration and reproduction chain are not perfect, hence with real world records there is no hope to really reproduce the live event.

Anyone that has listened to live non-amplified music knows by direct experience what the professor said.

Interesting question, I do believe the student is partly correct. Some of the electronic systems today can record information that is way outside the human hearing range and reproduce it too. The problem is that the recordings are usually done with multiple pick-up points (ie microphones) and the resulting multitrack recordings are then electronically mixed for the delivered product. The live performance though offers only two pick-up points, usually less than a foot apart (ie your ears). A lot of the experience though in the live performance is how the building mixes the sounds. Also with the live sound, the subsonics would be a bit more pronounced and the experience will differ depending upon where in the building you are located. If you consider all of this, the live experience will be different than a recorded one.

"the beat frequencies will be recorded in any case."

Why/how would they be recorded if only the original high frequencies (outside the range of the reproduction chain) were actually present in the first place? (I'm assuming that the recording equipment was of sufficiently high quality not to generate not-pre-existing sub-tones)

This comment stimulated some thought re the semantics involved. I think the term "beat frequency" suggests a wave with a frequency. When we say that the beat frequency is 5Hz when we compare 440Hz with 445Hz there is no 5Hz sine wave present. There is simply an amplitude variation which occurs 5 times per second. As the traces in post 33 show, there is no audible sine wave in any of the three traces. If we could hear 30,000 tones, then we'd hear a 30,000 tone, varying in amplitude 5000 times per second. Nowhere in the air is rarefaction and compression occurring at 5000 Hz. When we tune a violin, we do not need to possess hearing that responds to 5 Hz "tones" (sinusoidal triangular, square, etc. waves) because there is no such "tone", i.e rarefaction and compression is not occurring at 5Hz.

Once we get further out of tune, the growl we here at 10, 15, 20, and 30 Hz is also not the equivalent of 10, 15, 20, and 30 Hz tones. Obviously, the 20 Hz amplitude fluctuation is very easily heard, whereas a 20 Hz tone (and below) is nearly impossible to hear even at very high sound pressure levels.

A midrange speaker, fed the third of Randall's traces, would do nothing: it can't move fast enough to play the 30,000 tone, and the 5000Hz variation in amplitude can't occur if there is no tone to play.

A University of Wisconsin site says this :

Note that there is no wave present at the beat frequency. This can be illustrated by using two frequencies above the audible range of hearing but adjusted so that the beat frequency is within the audible range. Actually, if the sounds are sufficiently intense, it is sometimes possible to hear the beat frequency of two inaudible sounds because of nonlinearities in the ear.

(bolding mine)

I could take this to mean that my stance is usually correct, and that your's is occasionally correct, under very special conditons... but the Doublemint people would certainly say: "Stop! You're both right."

The professor may have been speaking in psychoacoustic terms more so than in physics terms. When we "hear" a beat of 15 Hz, (between 440 and 455) there is nothing in the ear flapping around at 15 Hz -- but it sounds to us as if there is. If the frequency of the beat gets up to 100 or 200 Hz, then it sounds very much like a tone of 100Hz -- but again, there is nothing actually vibrating (moving in and out) at that frequency. So, in a way, it is an auditory illusion, I suppose.

If we take the 30,000Hz tone with 5000Hz beat (in Randall's third trace) we both agree that if the electrical signal generating the trace were run through a rectifier, there could be an actual vibration caused in a speaker driven by the resulting signal. The amplitude of that signal would be equal to the amplitude of either of the two contributing signals. We also agree that there could be non-linearities that distort the third trace out of its symmetry. However, I suspect that the concert hall itself and the microphone contribute their own non-linearities -- but grant that these would be different than those of typical ear.

We have only subjective tests (I think) that indicate that adding in hypersonics improves the fidelity of sound. We have many objective tests that show that speakers, especially, contribute to measurable decreases in fidelity. Compression in the recording process is also measurable, and frequently dramatic, to even a relatively untrained ear. So while the professor is correct in stating the there could be a difference in the beats perceived live vs recorded, I think we agree that there are likely to be other, more dramatic, factors that render the recording only an approximation of the real thing.

I could take this to mean that my stance is usually correct, and that your's is occasionally correct, under very special conditons... but the Doublemint people would certainly say: "Stop! You're both right."

I suppose there is a certain dignity in the "Doublemint" response. On the other hand, it is so rare that I disagree with both Fyz and STL... and so rare that STL and Fyz take the same position, that, given the official answer, I'm inclined to write "Nah nah nah nah nah nah!"

But of course, I would never be so silly as to actually write "Nah nah nah nah nah nah." My sense of decorum prevents me from writing "Nah nah nah nah nah nah" ... at least any more than three times in a single post.

On the other hand, it is so rare that I disagree with both Fyz and STL... and so rare that STL and Fyz take the same position, that, given the official answer, I'm inclined to write "Nah nah nah nah nah nah!"

And so rare that you actually agree with the official answer. So, who is to say that the official answer is "right"? Especially not you!

I believe that the official answer, although referencing the Wikipedia article on "beats" , totally ignores the information in that article on "difference tones" and its links to another Wikipedia article on "combination tones" that describes the phenomenon more fully.

I will grant that I was mistaken about the nature of the beat waveforms, however the fact remains that these difference tones are produced, even if as a distortion, by parts of the human body, including, but not limited to, the inner ear, and could also conceivably be recorded as a distortion by some other instrument, such as a microphone, since the distortion itself is created as mechanical energy in the audio frequency range, even if the original tones were above normal hearing.

By the way, "Nah nah nah nah nah nah" are used as words to several songs, like Centerfold by J. Geils. The proper derisive beration would by "Nyah nyah nyah, nyah nyah, nyah!", possibly followed by a "Bronx Cheer", better known as the raspberry, rasp or razz, and sometime spelled (as in the comic strip "Bloom County") as "Thbbt!" or illustrated with the emoticon as follows:

:p

And so rare that you actually agree with the official answer. So, who is to say that the official answer is "right"? Especially not you!

Drat... foiled again! I was hoping no one would notice. Although if I recall, I think I did agree with the official answer on a challenge question I authored.

...a "Bronx Cheer", better known as the raspberry, rasp or razz, and sometime spelled (as in the comic strip "Bloom County") as "Thbbt!"

Because CR4 is a technical and scientific forum, we should hold to the proper decorum. This sound you refer to is known as a "bilabial fricative". Any long time George Carlin fan knows this.

The student is correct - although the professor's basic data** is correct - that the presence of ultrasonic frequencies can improve the aural experience. The problem is that the professor is advancing two contradictory hypotheses - that the perceived difference is purely due to beat frequencies, and that normal hi-fi repoducers cannot simulate the results.

Specifically, if he is correct that the benefit is due to the generation of beat frequencies, these frequencies can be artificially generated and added to the hi-fi signal, making hi-fi sound the same as the real thing. So, if he is correct that hi-fi that is limited to output in the normal hearing range can never sound the same as the original, then the reason for this cannot simply be the generation of beat frequencies.

**Recent reports indicate that people are more comfortable listening to very loud music if the sound contains some ultrasonic component. So it appears that the professor is right that ultrasonic content does affect the listening experience

Now for some unnecessary detail:

Difference frequencies can only be perceived as beats if the differences are generated, which need both frequencies to be present at the non-linear generator. The beats we usually hear are generated largely in the nervous system - after the sound has been sensed by the hair-cells; this beat generation can only occur between frequencies that we can actally hear. It has the interesting property that the perceived level of the beat is similar to the levels of the frequencies that generate it.

Another place that non-linear interactions can occur is in the hair-cells. Unlike what is described above, the original tones don't need to be audible. However, the level of the beat is proportional to the square of the input intensity, so these will only be perceived at relatively high listening levels.
It has also been speculated that hypersonic content may be detected by direct conduction and non-resonant sensing - in that case, although they are not "heard" as such, they still form part of the listening experience.

I believe that experiments have been proposed that shift the hypersonic frequencies, but it is not clear how these would discriminate between the two mechanisms, given that high overtones do not necessarily display well-behaved harmonic relationships. Maybe time-varying randomised shifting would do the job?

If point 2 were true you could sit at a location of the room with the piano playing, then substitute a bank of speakers that represent the same apparent angular size as the piano in place of the piano and they would sound the same in the same room (point 1). No?

In that case what would be the acoustic difference between the two setups?

This is not germane to the question but it does touch on some points of the topic being discussed, so I am not going to mark it off-topic.

Most symphonic recordings of live concerts are produce with a standard array of microphones that a recording engineer later mixes down to a single left-side/right-side two-channel stereo (or 4-channel for "Surround Sound").

However, a few years ago experimental recordings were done using a single pair of microphone mounted in an acoustic base that attempted to simulate a human head, complete with ear appendages and an internal mass (to simulate bone conduction), all in an attempt to reproduce EXACTLY the experience of a concert-goer.

Unfortunately, this type of recording could only be successful if the reproduced sound was created at a point similar to where it was recorded. i.e. effective playback could only be realized using headphones. This was perhaps 20-30 years ago, even before the advent of audio distribution via digital media, but I had read that the results were astounding, and you really felt as if you were in the actual concert hall attending a live performance. Of course, played back through speakers, the effect disappears and you simply have a very good classical music recording, albeit one that had not been tweaked by a recording engineer. I am assuming for this reason the recording technique never caught on.

I believe that I read about this in Popular Science Magazine, but it might have been somewhere else. If anyone knows whether this method is still being used anywhere, or has more information, it might be interesting as a thread itself.

A google on 'Dummy Head' produces interesting information

I remember the recordings made with two mics in the "ears" of a head. About 12 years ago a classical station near Charlotte NC--WDAV?--broadcast a regular show featuring those recordings.

I also remember the liner notes from a late '50s vinyl recording by the Firehouse Five plus Two. It said that the record had frequencies above 100kHz and that the better the reproducing equipment, the better the disc would sound, even if you couldn't actually hear the top end. Part of the effect was that, with vinyl, there's a rolloff rather than a cutoff of high frequencies. Better playback equipment whose own rolloff was very high wouldn't cause an artificial reduction of the highs. The natural rolloff, rather than beat frequencies, is likely the cause of the better experience at a live performance.

I knew there was a reason that I prefered vinyl, pops, hisses and all.

I did not read all of the answers, but I think you are missing the point. As long as the microphones can pick up the normal audible frequencies then the beat frequencies will appear to the person listening.

The beat frequencies are produced by the eardrum reacting to the audible frequencies impinging on it.

The beat frequencies are produced by the eardrum reacting to the audible frequencies impinging on it.

Gee, then how are radio frequency (RF) beat frequencies produced? Surely not by antennae reacting to frequencies impinging on them?

I believe that audio beat frequencies are a measurable artifact of sonic energy whether or not a human eardrum is present. It is produced by the creation of an energy pattern (wave) created by two (or more) energy patterns superimposed on each other, resulting in a new pattern of nodes and anti-nodes. RF energy will do the same thing.

STL:

I was always taught that, if you sum two sine waves in a linear element, they remain two sine waves. A scope or graphical representation may show reinforcement patterns, but the sum and difference frequencies don't really occur except in a non-linear element......like the detector in a radio receiver.

DickL

Sounds like (forgive the pun) it's just like the old question: "If a tree falls in the forest, when no one is around, does it make a sound?"

Kind of depends on your definitions.

I believe the significance lies in whether the beat frequency can be filtered out.

Take for example two sine waves 800 and 860Hz. Now, lets sum the two sines and run it through a 100hz high pass filter. If you are correct, you would not be able to hear a beat frequency. So what would you be left with? I think it becomes obvious when you think about it that you are left with the interactions between the two sine waves, this being the beat frequency.

The complex waveform you see on the scope is exactly what the cone of a speaker does (or at least tries to do) when driven by that source. So it is really the sum of the two sources.

Or an ear drum

tom

=-==

I believe Constructive and Destructive Interferrence are the terms you are looking for.

Without nonlinear interaction, constructive and destructive interference will not excite a resonator at the difference frequency.

your argument makes sense, but then I see this product

http://www.atcsd.com/pdf/HSS-Manual-Website.pdf

Which is a real, on the market, honest to goodness product, and I wonder how it works. It says they use a 40-50kHz carrier, which is way above human perception.....

From the specification it appears to be similar to an amplitude modulated ultrasonics (45-kHz) signal, probably using carrier and modulation levels that depend on the amplitude of the 'sound' required. Pompei's company claims that the nonlinearity their system uses is in the air itself - which would imply very high ultrasound levels. This theory would be supported by the poor low-frequency responses of the systems; however, there are other perfectly plausible explanations for the low-frequency deficit**. So the alternative theory (asserted in US Patent 6631197, for example) that demodulation relies on non-linearity in or around the ear is also plausible. In either case, if the perceived sound is to reach 100-dB SPL, the ultrasonics level could be appreciably higher - perhaps even higher power-density than the audio-frequency pain threshold??

**I've not been able to find any publications on this - but it would be conclusive if the sound is not audible near the transducer; alternatively, if the low-frequency cut-off varies inversely as the beam diameter (while it exceeds the size of the listeners head), that would demonstrate that at least part of the effect is due to interactions in the air. [N.B. The system is supposedly suitable for in-car use, which I think means that this explanation would need more substance before I would regard it as the most likely]

I think the Audio Spotlight (Holosonics) explanation of this effect is pretty good. To verify that the non-linearities occur in the air, and not in the ear, I called their engineering department. When I asked if it would be true that the vast majority of the non linearities occur in the air, the person I spoke with said: "Actually, not just the vast majority... 100%." When asked if one could then reliably record the sound (within the beam) with an ordinary microphone, he replied, "Yes, of course. In the air it's just ordinary sound; only the way it's created is different."

Therefore, as Llero says, you should not expect there to be differences in the recording and the live performance due to this effect. There are other very dramatic and measurable effects for many of the differences.

Do we perceive ultrasonics via some means other than hearing (such as through skin nerves)? Perhaps -- in fact there are gizmos built on the premise that this occurs. Testing the Neurophone would seem to be quite simple, but there is little on the web that indicates that it works, and little to indicate that it clearly does not.

I expect that Holosonics' engineers truly believe this. But I've failed to find any publications (either experimental or theoretical) to support this - and their competition (who appear to be ahead in the marketplace**) appear to work on the basis that the sound is generated at the 'listener'.

**Of course that could be because they have a different product strategy - such as pursuing cost before performance.

BTW, thinking back to the distortion in some horn-loaded loudspeakers, my unreliable recollection is that these required levels equivalent to 140-dB SPL for air-distortion levels to become significant

I agree that non-linear interaction can occur in the eardrum itself, but expect the interaction at high frequency to be relatively slight (due to the relatively low wave velocity across the drum). This was why I concentrated on receptors such as hair-cells as potential sources of beats between ultrasonic signals. However, I have no data to support this assumption, so the ear-drum could indeed be dominant here.

However, your implication that the eardrum is implicated in most cases of mixing of auditory signals to provide a beat-tone is clearly false (neither would hair-cells be involved). The evidence can be found in high-school experiments on the production of audible beat-tones. These use a pair of input tones of very similar levels, and a difference-frequency beat is heard at similar intensity to the input tones, regardless of the levels of the inputs. This is incompatible with non-linear interaction of the original tones, as the level of the generated difference frequency will always rise faster than the levels of the signals. This means that the mixing that causes the subtone has to be at a point where the levels have been brought back to a standardised level; as there is no mechanism in the mechanical structure of the ear that is capable of performing amplitude correction, the interaction that causes us to hear these difference tones cannot actually be occurring anywhere within the mechanical system (at least, not until the sound level grossly exceeds the level at which these experiments are typically performed).

As a general reply:

I think the professor's claim is a fallacy of logic and that is the crux of the puzzle.

You can argue the nuances of audio reproduction, but that is not what I think the fallacy actually is nor what the author of the puzzle is after.

Agreed! The sense of the question isn't the technical evaluation of the nuances of the acoustic system, but the question of cause and effect, when the cause isn't within the detection powers of the recording device, but the effect is.

The copy never will be exactly the same as the original, but that's not what the question is.

First of all, the proffessor is always right, at least in the GlobalSpec challenge....

Second, most of the hi-fi's sharp crossover at 20k is Designed to eliminate frequencies above 20k from entering, while the ear's limitation is only it's inability to transduce above a specific freq., the higher freq.'s DO enter the ear, strike the drum, and there-in beat out the difference freq. in the transducable range.

tom

=-==

The beat frequencies are present in the orignal hall, and therefore are 'heard' by the microphone and recorded. They exist in the recording. The prof is wrong. The acoustics of the orginall hall will be hard to reproduce. The microphone will experience the same sounds as a listener, but each microphone is independent, in humans the brain 'connects' the ears into a total sound stage. Only when the the sound is re-created by as many point sources of sound as the orignal and in a similar acoustic space, could a believable reproduction be made. Perhaps the answer lays in the number and placement of speakers and microphones, and number of active channels.

A little off topic? but perhaps a subject of another challenge - A listener stands in line, and beyond the end of a runway, facing away. A plane takes off. How does the listner know the place was to the rear, then overhead, then in front? The sound arrives at each ear at the same time ! (forget body effects - eg: use the sound of a bee, one can still tell if it's front or rear)

I can't back this up, but I would guess is has something to do with the asymmetrical shape of our ears. when sound approaches from the rear, the directional high frequencies will be slightly reduced, therefore giving the brain a clue as to whether the sound is coming from in front or behind.

Just so we all know what we're talking about here (hear?)

I don't think there is any part of the ear which can demodulate the higher frequencies.

There is apparently evidence that we have some means of sensing the presence of ultrasonics that are related to what we hear. (But the student's complaint is still correct - the professor's statements were self-contradictory.

I don't think there is any part of the ear which can demodulate the higher frequencies.

I agree. To hear the 5000 Hz beat shown, you'd need the equivalent of a rectifier in your ear.

I agree. To hear the 5000 Hz beat shown, you'd need the equivalent of a rectifier in your ear.

Putting aside the fact that the amplitude is probably very low, as A.H. described, why couldn't you hear a 5000 Hz beat? Doesn't it manifest itself as a 5000 Hz tone (which is in the audible range) in an audio speaker, or am I missing something? (Maybe I skipped Physics class that day!)

If I send electrical pulses to a speaker from a variable frequency oscillator, and begin at 1 Hz. I should hear a slight popping noise once every second. If I increase the frequency to 10-20 Hz, I might then feel a vibration. At about 50-100 Hz I will hear a low, rumbling tone. The 88 keys of a piano range from 27.5 Hz to over 4000 Hz, so at 5000 I should hear a tone somewhat higher than the highest key on a piano.

The Wikipedia article on "Beats (acoustic)" had this to say about the phenomena:

Difference tones

Consider the two waves starting in unison, f = 0. As the difference between f₁ and f₂ increases, the speed increases. Beyond a certain proximity (usu. about 15 Hz), beating becomes undetectable and a roughness is heard instead, after which the two pitches are perceived as separate. If the beating frequency rises to the point that the envelope becomes audible (usually, much more than 20 Hz), it is called a difference tone. The violinist Giuseppe Tartini was the first to describe it, dubbing it il Terzo Suono (Italian for "the third sound"). It is not surprising that this was first discovered by a violinist: playing pure harmonies (i.e., a frequency pair of a simple proportional relation, like 4/5 or 5/6, as in just intonation major and minor third respectively) on the two upper strings, such as the C above middle C against an open E-string, will produce a clearly audible C two octaves lower. Disintonation, including a major third in equal temperament, makes the sound gruffy and rough.

An interesting listening experiment is to start from a perfect unison and then very slowly and regularly increase the pitch of one tone. When one tone starts to split out from his former twin-note, a slow rumbling can be heard, gradually increasing into an audible tone.

Get that? The beat DOES become perceived as an audible tone when it falls in the audio range!

Get that? The beat DOES become perceived as an audible tone when it falls in the audio range!

Duh. If both tones are audible, you hear a beat, that turns into a growl as the beat frequency itself get above 20 Hz. But that growly noise does not change in perceived pitch after is gets up into the 200Hz range and above -- you don't hear A 440 in the background when you set two tone generators 440 Hz apart: 6000 and 6440, for instance.

If the tones generating the beat are themselves inaudible (by frequency) but high amplitude, you hear no beat frequency. You can prove it to yourself with a dual tone generator, the link for which is provided in post 42.

Set the tones for high amplitude, wear earphones if you think your speakers can reproduce the sound adequately, and listen to the difference tone between 14,000 and 15,000. You will hear nothing, and certainly not a tone at 1000 cps. If you look at the post of the apparent 5000 Hz beat between a 25,000Hz signal and a 30,000Hz signal, you can see that its amplitude is very high: rectify the signal, and you'd hear it. Without rectification, you'd hear nothing.

Re the above... of course you can hear difference tones, if the underlying frequencies are audible. If they are not, then you hear nothing, just as you hear nothing if you leave the rectifier out of your crystal radio.

But prove it to yourself: use the dual tone generator, and set one frequency to above your hearing limit, the other 1000 Hz higher. You will hear nothing, but you should hear, per you contention a 1000 beat. If you have a scope, you can put the two frequencies in and see something virtually identical to the previous post w/ 25,000 and 30,000: a very high amplitude beat (or difference tone per above nomenclature) the envelope of which is at an audible frequency. But you hear nothing -- even with my fancy earphones which are less than 3db down at 20,000 Hz.

That isn't an argument, that's just repetition.

I give up. Your're right. Have a nice day.

I wasn't merely repeating the argument, but making it a little simpler, so you could understand.

When you wrote:

Putting aside the fact that the amplitude is probably very low, as A.H. described, why couldn't you hear a 5000 Hz beat? Doesn't it manifest itself as a 5000 Hz tone (which is in the audible range) in an audio speaker, or am I missing something? (Maybe I skipped Physics class that day!)

... i took that as a profound misunderstanding of amplitude modulation, the principal on which AM radios work. As Randall correctly points out in post 33, you would not hear a 5000 Hz tone, even though the amplitude of the beat envelope appears high -- however it is not: every upswing in the envelope is cancelled by a symmetrical downswing. The 5000 Hz tone is encoded in the envelope just as audio waves are encoded in an AM broadcast: you don't need to be able to hear 660KHz to hear the audio -- but you must rectify the signal to decode it. The rectifier takes the symmetrical envelope (which is by itself inaudible -- even though the envelope looks audible) and allows just the upper half through, and voila, the lower and upper half of the waveform no longer cancel! The Sound of Music!

Apparently you did not take the opportunity to prove this to yourself with a dual tone generator -- thus I repeated the suggestion, fearing you'd missed it. Another experiment you probably did in physics is with two speakers producing the same tone. In locations where the sounds are perfectly out of phase, there is silence. The envelope in Randall's post is like two out of phase sounds: there is nothing there to cause a sound our ear could hear.

But don't take my word, or that of Giovanni, who was speaking of audible fundamentals. Load a dual tone generator, plug in earphones, and have at it. Unless your hearing is a lot better than that of most people your age, a generator which goes up past 14,000 or so is plenty good enough -- and earphones (and even crummy computer speaker tweeters) are adequate for producing the fundamentals (14,000 and 15,000) as well as the 1000Hz tone you might think would be produced... but all you will hear is silence.

The best possible case for showing that the professor might be right would be with the high amplitude signals you can get fro a generator. For the very low amplitude ultrasonic harmonics from instruments mixed in with loads of other frequencies, echos, phase distortions, etc. the likelihood of sensing anything at all re beat frequencies would have to be very very remote. So,if you can't sense it in near perfect lab conditions: plenty of amplitude, just two simple frequencies producing a 1000 Hz beat, how could you hope to sense it in a concert setting?

A beat frequency varies the apparent amplitude of something you can hear.

Try this: Make an adapter cord for your headphones. Make it about a foot long, with a mini jack at one end, a mini plug at the other. In the middle of one of the two leads insert a rectifier. Try the 14,000/15,000 test first without the rectifier, then with the rectifier. Report back.

BTW -- everything is just a repetition of something else.

Why do you continue to insist that rectification is needed - do you redefine all non-linearity as 'rectification'?

Fyz

... i took that as a profound misunderstanding of amplitude modulation, the principal on which AM radios work.

No, in fact, as a licensed Amateur Radio Operator I have an excellent understanding of the principle of amplitude modulation.

I also know that when you mix an audio frequency (AF) signal with a radio frequency signal (RF) your resulting products, besides the original AF and RF signals, will include the sum and difference of their two frequencies. These are called sidebands and is the basis of Single Sideband AM radio (SSB), the backbone of HF/Shortwave two-way voice communications for the last 50 years or so.

When the AM radio signal is processed the extremely low AF energy is naturally filtered out leaving the original RF signal (known as the carrier wave) and the two sidebands. In SSB communications the carrier wave and one of the two sidebands are eliminated, or, more properly, suppressed to a level where they are essentially non-existent. Now that the original signals are gone, does that mean we have eliminated the "beat frequency" energy? On the contrary, it is the sideband that remains which IS this "beat frequency" energy, and it alone gets amplified and transmitted to a receiving station (thus saving a lot of energy that otherwise goes into the carrier wave and the other sideband in standard AM broadcasting) making SSB a much more efficient means of transmitting voice communications. Yes, the original audio is "encoded" and not actually present, requiring rectification, but only after the AM signal is re-created by injecting a synthetic "carrier wave" in the receiver. Likewise, a BFO, or Beat Frequency Oscillator, is used to create an audio tone for an operator to decode the on-off keying of the carrier wave in Morse Code, or CW (Continuous Wave), communications. This is done by "beating" another RF signal with the received CW signal, creating an audio signal from the difference between the two RF signals. This audio signal can then be detected with headphones or amplified and fed to a loudspeaker. It exists as electrical energy until it is detected by headphones or speakers, just as the beat frequency "difference tone" exists as an air pressure wave until it is detected by the human ear/brain system.

That is what I meant by referring to the "If a tree falls in the forest..." question. If we define "sound" simply as a phenomenon experienced by the human inner ear and detected by the human brain, then a tree falling in the forest makes no sound if no human is around to hear it. But if we define sound as a mechanical pressure wave in air or some other medium, then YES, the tree makes a sound!

Never mind losses at the recording, it is simply impossible to reproduce two "pure" notes with a looadspeaker when the lower frequency note introduces the doppler effect on the higher frequency note. The sum total of many notes being put through a simple loadspeaker is at best a poor copy of the original.

The professor is wrong. period.

Think of it this way:

At the live performance you have multiple point sources of the sound, from each individual instrument.

If, after recording with mikes placed at each instrument, you then play back the recording in the same room, you will have only the # of playback speakers as your point sources. Very different sound and feel!

Hard lesson learned while working as recording engineer for US Army morale support activities when I was stationed in Germany.

However, you can come close to reproducing the original "feel" (for lack of a better term) of the original performance by individually recording each instrument then playing back through individual speakers placed at the location of each of the performers as they would have been in the entire ensemble. But, taking into account the losses introduced by the recording medium you will still not duplicate the sound and feel of a live performance.

charlie

Definitely, the student is right. We will hear the effect, including the beat frequencies, but not the cause. Per Aristotle, Thomas Aquinas, Anselm of Canterbury, and others; for every effect, there is a cause, even if we don't know what the cause is.

If the limiting factor is the recorded reproduction, and if the recording equipment indeed does record the full range of human hearing, even if it can't pick-up the higher frequency, the recording will include all the frequencies hearable by the human ear, which INCLUDES the beat frequencies. The beat frequencies will be within the recording range, even if the recording doesn't pick up the higher frequencies that caused the beat frequencies to exist. The microphone and recording equipment will process the effect, just not the cause.

... of course the recorded sound will never be a perfect representation of the original, so in that since the professor is right. As the $ and technology goes up, the quality of the recording will get asymptotically closer to the original sound, whatever specific technologies are used.

In the sense that the recording will pickup the audible beat frequencies, the student is right. I think this is the crux of the question, and not the question of exact representation of the original.

Do you suppose that the "missing" beat frequencies exist in the absence of the non-linearities in or near the ear?

I think the professor is a nut case. We can only "hear" beat frequencies if the fundamentals are within our hearing range. In the same way, we cannot hear an AM radio station unless there is a rectifier in our radio circuit.

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So, if the professor is trying to say that the main reason that a live performance sounds different than a recording is because we can hear beat frequencies of otherwise inaudible harmonics, I'd say he is wrong. The principal reason for the difference (of which there are many) is dynamic range. At each step in the recording and reproduction process (via mechanics of the mike, S/N ratio of the electronics, etc) dynamic range is decreased, so much so some would argue, that recent recordings are almost unlistenable.

BTW, you can play with this sort of thing on your computer using a dual tone generator like this one, which I downloaded without any incident (like attached viruses, etc).

If you set the generators to (let's say) 14,000 and 15,000 (and if you are as old as me) you will hear nothing, even though you might think that the 1000Hz beat would be audible. You can also experiment with lower beat frequencies. When the beat frequency is a few Hz, you hear the expected "beat" used in tuning musical instruments. When the beat frequency itself gets to the range of 20 Hz, it adds a growl to the sound -- you can tell you are hearing an additional frequency but that frequency does not seem to have a "pitch". When the beat frequency is varied around 100 - 1000 Hz the nature of the sound seems to change only slightly -- in other words you don't hear an apparent frequency change, and in fact, you hear very little difference at all.

BTW, you can change the frequency by single Hz with the arrow keys.

Yes, the professor is talking nonsense.

But there is some nonlinearity in every system, which will generate difference tones in the hearing system before it has opportunity to filter the sound. You don't specifically need a diode - anything that has second-order non-linearity will do. So you will definitely hear difference tones between sounds that are too high in frequency to hear on their own - if the amplitudes are high enough. The professor may even be correct that this is the reason that blind-blind studies have shown that very loud music is more pleasant to listen to (sounds more natural?) when ultrasonic frequencies are reintroduced. The reason we know that the professor is talking nonsense is that, if the improvement is caused by perception of the difference components, these could be artificially recreated within the audio band of hi-fi systems; in that case the absence of ultrasonic components would no longer be the cause of the lack of apparent fidelity.

(Of course, perfection not being possible, it cannot ever sound exactly the same as in the hall. However, as halls vary, it could still sound better than in my local venue)

BTW, the best reproduction I have heard used recordings made with a single pair of "crossed" microphones (a "Blumlein pair"), and reproduced in a very large room using a large pair of electrostatics. The desire of recording engineers (and possibly producers and conductors too) to control the individual balance by using multi-miking led to a definite degradation in realism - never mind additional bad habits such as truncating the dynamic range (though I admit this can be helpful if you have to drive while you are listening).

So you will definitely hear difference tones between sounds that are too high in frequency to hear on their own - if the amplitudes are high enough.

Hey, Fyz! For once we agree. Tell Blink to go soak his head! Then maybe he will get the wax out of his ears that is keeping him from hearing the difference tones!

Hi STL

Give Ken a chance. I think we must all be allowed to be mistaken from time to time. On the other hand, persistence down such a path without apparently considering the issues can become irritating.

N.B. Mightn't wax enhance the difference tones? It's mechanical behaviour is, after all, notoriously non-linear.

Fyz

Mightn't wax enhance the difference tones? It's mechanical behaviour is, after all, notoriously non-linear.

Yes, as long as the air passage did not become completely plugged. Weren't conformable ear-plugs, before the little yellow (now many colors) foam type were invented, usually made from wax and paper? I think it is a fairly effective sound attenuator.

And I am being kind. I could have suggested that he remove another substance from his ears! On the other hand the problem may not be what is IN his ears, but what is BETWEEN his ears!

Weren't conformable ear-plugs, before the little yellow (now many colors) foam type were invented, usually made from wax and paper?

Definitely off-topic here, but I couldn't resist telling this story:

Back in the 1970's when I was a young Airman serving as a Medical Technician on the USAF C-9A Nightingale (Hospital aircraft), we would hand out a pair of pink wax and paper moldable ear-plugs for use by passengers and patients. The Air Force version of the DC-9 did not include as much sound insulation as the civilian version and it could get quite noisy. This was especially so in the passenger section between the two engines on the side of the fusilage at the rear.

On more than one occasion I had to respond to a passenger trouble light (just like the ones on civilian airliners) when a passenger would complain that his pink chewing gum tasted awful!

So you will definitely hear difference tones between sounds that are too high in frequency to hear on their own - if the amplitudes are high enough.

Not in practice. Consider the difference tone in post 33: 5000Hz. Its apparent amplitude is high: the difference in envelope height that creates the 5000 Hz tone shown, is large. But you would hear nothing. Similarly, if you download the dual tone generator (which is very accurate, BTW.) you can play two tones at very high amplitude (to which my dog will attest) but the beat frequency is entirely inaudible, whether is is 20, 100, 1000, 4000, 5000Hz etc. I you have a good mic, you can plug the combined sound back into Windows Recorder, and look at the waveform, to verify that your transducers are really making sound.

Randall's correct: we don't have mechanisms in our heads that will create an audible beat frequency out of two inaudibly high pitched sounds. Put a diaphragm near a speaker producing the beat frequency shown in Randall's post, and it will not move in and out at 5000Hz: the shape of the envelope tells you that, with the upward bumps neatly cancelling the downward ones. If the diaphragm is sufficiently small ans light, it will move in and out at 30,000 Hz, with the amplitude of that motion varying at 5000Hz. (The diaphragm moves only with the in-out waves, not with the apparent envelope wave. It is an entirely different scenario from superimposing a 5000Hz tone on another.)

Using the dual tone generator, when the frequencies are audible, the beat frequencies are very clearly discernible: set the tones 1Hz apart, and the wah wah is pronounced, as is the growl at 20 Hz.

Hmm, it appears for once that STL's instincts were right - you are now re-asserting your case without either taking the trouble to answer theoretical objections that were directly addressed to you, or apparently to verify your statements.

Clearly, you don't need rectification - any simple non-linearity will be sufficient to down-convert pairs of suitably-spaced ultrasonic signals into the audio region, as I demonstrated with my school-level trigonometric equations in post #52 - let me know what about that was not clear if need be. You must be aware that there are plenty of mechanisms between the outer ear and the hearing receptors that are sufficiently non-linear to perform the sort of conversion that is required.

Assuming that your headphones are capable of transducing both the incoming ultrasonic frequencies***, you will indeed hear difference tones when the ultrasonic levels are high (not knowing about possible side-effects, I wouldn't recommend listening like that for long, however). Only having tried this experiment** with headphones that were sufficiently large to surround the outer ear, I couldn't swear that this would be the case when using smaller headphones - it could be that the outer ear absorbs the ultrasound, and that it actually needs to be transmitted via bones. What is clear is that we do have mechanisms within our heads that can create difference tones between frequencies that we cannot hear directly. Indeed, if you can find me a physical structure that exhibits linear behaviour when excited with very large signals, I will show you a vacuum.
** This was many years ago - I don't currently have access to the right sort of equipment, unfortunately. Similarly, we didn't try the experiment that would now interest me - to play one frequency only into each ear - we should then only have down-conversion if the ultrasound is conducted across the head...
***The best way to check is to use the two headphones of the pair as loudspeaker and microphone respectively. But you need to be careful about electrical crosstalk - if you have the phones in fixed positions and there is only a small change in response when you place a sheet of material in the way, then what you are seeing is more likely to be crosstalk than ultrasonic transduction. Incidentally, this was how we checked that the perceived sound level was not actually the result of down conversion by non-linearities in the headphones.

Hmm, it appears for once that STL's instincts were right - you are now re-asserting your case without either taking the trouble to answer theoretical objections that were directly addressed to you, or apparently to verify your statements.

Actually STL's instincts have been right more than once. I remember a time just over a year ago...

I believe I did take the time to verify my statement that the 1000 Hz beat frequency between 14,000 and 15,000 is inaudible (for someone, like me, for whom those frequencies themselves are nearly inaudible). I performed the experiment, and could hear no beat frequency of any sort, 1000Hz or otherwise. In this experiment, the audio levels were set quite high (enough that with the frequency turned back down to 10,000 the apparent loudness was high.)

Clearly, you don't need rectification - any simple non-linearity will be sufficient to down-convert pairs of suitably-spaced ultrasonic signals into the audio region, as I demonstrated with my school-level trigonometric equations in post #52 - let me know what about that was not clear if need be.

I don't think any simple non-linearity is sufficient. In my experiment, I did not possess sufficient non-linearities, even when moving my head around in front of speakers or when wearing enclosed headphones. What non-linearity do you have in mind that would make me hear a 1000 Hz tone? For that tone to be clearly audible, I'd think I'd need something close to a diode, the response of which I have generally thought of as being fairly linear with respect to frequencies under 100,000Hz. By non-linear do you mean non-linear in frequency response?

Your argument, extended, would mean that the diode in a crystal radio is unnecessary, wouldn't it? The added waveform in post 33 is effectively that of an amplitude modulated 5000Hz tone on a 30,000Hz carrier. If I wanted to clearly hear the 5000Hz tone at high amplitude then I'd need something very close to a diode, rather than an assortment of non-linearities, I'd think.

I can imagine conditions under which I could hear sound information carried on ultrasonics... but is that the reason a live performance sounds "live"? I don't think so.

Were there other theoretical objections addressed to me that I have not taken the trouble to answer?

"I believe I did take the time to verify my statement that the 1000 Hz beat frequency between 14,000 and 15,000 is inaudible (for someone, like me, for whom those frequencies themselves are nearly inaudible). I performed the experiment, and could hear no beat frequency of any sort, 1000Hz or otherwise. In this experiment, the audio levels were set quite high (enough that with the frequency turned back down to 10,000 the apparent loudness was high.)"
That is quite a surprise - I did a similar experiment some years ago, though the frequencies I used were 24 and 26 kHz. And half-way decent headphones should not have zero-responses in the range you suggest. The only significant differences I can think of would be amplitude (as we are not using a diode, the non-linear output rises as the square of the input levels, and the levels I used would have been just below uncomfortable, rather than "quite high") or that my headphones were the type that completely surrounded the ear.

"By non-linear do you mean non-linear in frequency response?"
No, I mean amplitude non-linearity, as should have been apparent from the square-law non-linear equation.

"would mean that the diode in a crystal radio is unnecessary, wouldn't it?"
Crystal radios are designed to detect relatively low level signals without amplification, so you need a very strongly non-linear element - preferably an ideal rectifier. The diode comes close. Of course, the two-tone input is not like AM, so if you try to extract the difference frequency using a rectifier you will get all the harmonics of the difference frequency as well.
What we are postulating here is an effect at high signal levels, so any reasonable non-linearity would do the job.

"I can imagine conditions under which I could hear sound information carried on ultrasonics... but is that the reason a live performance sounds "live"? I don't think so."
If you believe that the referenced research was as claimed, it appears to be a necessary condition - i.e. your strongly implied "sole" in "the reason" is not relevant to the argument.

Other than that non-sequitur, there is nothing else you have not attempted to address.

It's very relevant. This nutty professor believes it is the main reason:-

" He claims this is because "

Neither of you appears to have addressed the question of whether or not this mechanical demodulation is more likely when the sources of the two interfering signals are spatially separated.

CR4 talking at cross purposes? Surely not...

There is a difference between "the reason a performance sounds live", and "a requirement for it it to sound live". Clearly, if the presence of ultrasonic frequencies is significant (as has apparently been demonstrated), accounting for them is just one of many requirements. Based on the best (only?) available work, the professor is right that the absence of ultrasonic content makes the sound appear less natural.

BTW, so long as our hearing does not have perfect resolution, his implied position that information processing could in principle create an indistinguishable replica of the sound you would have heard in the recording venue is correct**. It would of course require a better representation of the original than currently available, plus monitoring the position of your head and a great deal of information processing. The remaining question is whether you can achieve naturalness without adding in the actual ultrasonics - and if the professor's explanation of "the reason ultrasonics are necessary" is actually an explanation of why they might not be needed after all - as it leads directly to a method of substituting sound to achieve the same effect. (Of course, the ultrasonics could be sensed via a completely different path - in which case they would be needed, but the professor is wrong about the reasons.)

**I'm aware of a potential limitation - the sound delay between the speakers and our heads. Bit this is unlikely to be more than 1/50th of a second using current speaker positioning, so the errors in normal movement (due to acceleration) are likely to be insignificant.

There is a difference between "the reason a performance sounds live", and "a requirement for it it to sound live".

The professor said "that a live performance of an orchestral piece will always sound different from a high-quality Hi-Fi reproduction. He claims this is because in the live performance, the listener will be able to hear some beat frequencies..." He did not say "One of the many reasons that recordings sound different..."

If one is asked "Why is the sunset reddish?" it would be a rare person (technically aware person, that is) who would say "This is because there is pollution in the air." Pollution can contribute to sky coloration. A professor (we hope) would chose his words carefully to avoid confusing and misleading his students. There are many differences between a live performance and a "hi fi" (how hi?) recording that can be easily measured by instrumentation far more crude than required to ascertain the influence of inaudible frequencies. The most obvious of these major contributors are the speakers themselves, which cannot come close to recreating a faithful analog of the the electrical signal going in, let alone recreating the original spatial imaging. Even very good speakers are an order of magnitude worse than very good electronics.

I agree with most of that - the professor is clearly saying that here is a reason that you could never make realistic recordings using only audio equipment - maybe he just didn't get to finish his "even if everything within the audio bandwidth was ideal" statement before being interrupted. The question is whether his statement was correct. We can categorically say that is wasn't, because either he has the mechanism wrong (as you are convinced), or the mechanism would allow you to spoof the ear to believe the ultrasonics were present.

Even though I have observed ultrasonics mixing into the audio band, I strongly suspect that aural non-linearity is not the only mechanism.

One thing I hope we can agree on: we do not need to know whether mixing occurs to know that the prof is talking balderdash.

Ken:

I wouldn't describe the audio portion of this "sound" as a beat frequency, but here's a demonstration of the ear demodulating an ultrasound signal.

http://www.flixxy.com/focused-loudspeaker-technology.htm

There's controversy about whether the detection is performed by the ear or air, but it IS happening.

DickL

I think you could describe it as due to beating, because the mechanism is similar.

To my knowledge, systems have been developed where the mechanism is non-linearity in the air. These often rely on the ultrasonic beam being focussed, and the focus is kept away from the listener; in this case a normal-frequency sound is generated near the focus. The sound mainly moves in the same direction as the ultrasonic signal, but the audible frequencies do spread more than the ultrasonic beam (how much will depend on the relationship between the beam diameter and the wavelength of the audible sound).

Nonlinear interaction via the ear or via body surfaces is also possible; this would not require as high ultrasonic levels as audio generation in free air, and would be easier to make truly private. (But I suspect it would be more difficult to control the exact sound output, in case that matters)

The designers of any equipments probably do know which of the mechanisms they are using - but may be coy about this until they are fully confident of ownership of any intellectual property.
N.B. I would be concerned about safety if the ultrasonic levels are very high.

Back in the day (God, why do my posts start with that so often?), somebody like Bell Labs did a marvellous demo recording (I believe it was on a huge 78 rpm disc) where they added high frequency and low frequency filters to music. When they blocked everything above, say 60kHz, you could tell the difference. I no longer remember their explanation for why this happened, but it did.

"He claims this is because in the live performance, the listener will be able to hear some beat frequencies between some higher frequency harmonics (above the hearing range), whereas in the recorded reproduction (unable to record the original, high harmonics), the beat frequencies will not exist."

Can someone explain why that if the original frequencies can be recorded, a beat cannot be heard from the mixing of the re-played tones?

He's saying that hi-fi systems inevitably filter the ultrasonic frequencies, so the ultrasonic frequencies are not there in the replay. In that case, there are no original signals to stimulate the beat frequencies. But he's wrong on at least two counts** - if it makes a significant difference, either a way will be found to present artificially generated signals that sound as if the ultrasonics were there, or (if that is not practical) hi-fi will be redefined to include the appropriate frequency range

**Hi-fi enthusiasts being the perfectionists that they are

I'm not an acoustic engineer or a physicist, but this reminds me of an occasion when one of my musician friends had me listen to a comparison of a digital recording (CD) and record (33 1/3 RPM). Same stereo system (amplifier & speakers), two different inputs.

Without knowing which recording was which, one could definitely tell one recording had a richer sound -- it was the record. This was probably over 10 ago. Our hypothesis was that the people who created the digital masters "engineered out" subtle distortions that actually gave the music a richer sound.

I am curious, Mr. Guest. By "richer", do you mean that the sound seemed "fuller" with more tones, overtones, harmonics, etc, or that it was actually more pleasing and pleasant to listen to (or possibly both fuller and more pleasing)? Also, were you listening through loudspeakers or headphones?

Perhaps what you were hearing was actually the gradual roll-off of higher frequencies mentioned previously, rather than the sharp cut-off in digital recordings. Perhaps there is something in human hearing and sensitivity that allows us to feel an effect in our minds/brains from higher frequencies than what we can consciously discern. Haven't psychologist proven that hypersonics can cause discomfort to humans as well as animals if the amplitude was high enough? It would seem that a lower level of hypersonic harmonies could also have a pleasing effect as well, adding to the musical experience.

Wikipedia has a nice short article on the "Hypersonic Effect" that explains this better. It seems that there are two important points. One is that the High-Frequency Components (the hypersonic sounds) do have an effect on EEG patterns in the brain and, two, that people would could not consciously discern the HFCs by themselves still preferred identical musical recordings WITH the HFC's intact to ones with the HFC's filtered out. A later study showed that this result was not exhibited by people who heard the music only with headphones, but WAS exhibited by those who listened through loudspeakers, indicating that the HFC were taking an alternate route to the brain rather than through the ears. This is further explained in the article on "Ultrasonic Hearing" which describes how HFCs may reach the brain by stimulation of the base of the cochlea through bone induction rather than through the physical inner ear, as in normal hearing.

The professor's claim is that someone listening to a recording of a live performance will not be able to hear the beat frequencies because the beat frequencies will not be recorded. However, if the beat frequencies are first generated by the blending of the instruments' sounds in the concert hall, they will be generated again when the instruments' sounds are recreated by the loudspeakers or headphones.

Yet, the recording will sound different because the listener's environment will produce different reverberation effects than the concert hall.

BTW, Lleros MaHarg is Graham Sorell (or Sorell Graham) spelled backwards. I wonder if he's related to that Syhprum fellow...