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Set the Tone (July 2012)

Posted July 01, 2012 12:00 AM
Pathfinder Tags: challenge questions wavelength

This month's Challenge Question: Specs & Techs from GlobalSpec:

If the wavelength of bass tones is very large, how do small speakers (i.e. those in cell phones) produce these tones when the wavelength is several times larger than the speaker?

And the answer is:

When a sound signal is received by a linear system (linear response) only the fundamental tones (the ones actually present in the sound) are sensed or transmitted. However, if the system exhibits non-linear responses, not only the fundamental tones are sensed and transmitted, but the system also reproduces the harmonics of each one of the tones present in the sound. This means that the non-linear system reproduces the sums and differences of the whole number multiples of the fundamental frequencies. The system formed by the ear and brain is actually a non-linear system, so we hear a low fundamental tone (like in a human speech) and all the harmonics produced by the system, including the large wavelength of the bass tones.

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#1

Re: Set the Tone (July 2012)

07/01/2012 7:26 AM

Poorly.

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#2

Re: Set the Tone (July 2012)

07/01/2012 10:45 AM

Synthesized beats between pairs of higher frequency tones?

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#3

Re: Set the Tone (July 2012)

07/01/2012 12:47 PM

Actually, I think all that is required is that the acoustic surface be able to travel back and forth with a period equal to the period of the low notes. The tiny surface in these speakers is, effectively, just a small piece of a larger speaker surface that would produce the full volume of the tone. The small speakers can't produce the volume of sound that a 24 inch cone speaker can produce, but they can at least produce the note. And if you're wearing headphones, for example, the volume is pretty low anyway, compared to the volume needed to fill your living room or a concert hall.

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#39
In reply to #3

Re: Set the Tone (July 2012)

07/04/2012 12:35 PM

Just to add an anecdote:

I don't have a 'surround sound' system connected to my TV, but last month I did connect a fairly decent bookshelf stereo to the audio output from the TV. Then, as it happened, I decided to re-watch my DVD of the movie "Pi", which I'd watched a few times before. My reaction to the improved sound through the stereo was 'Wow!' The sound, esp the vastly improved bass of the techno background music, was fantastic. I'd missed so much of the movie before, when I'd listened only using the tiny (and tinny) TV mono speaker. The bass tones were 'detectable' through the small speaker, but dramatically 'There' via the stereo.

By the way - another analogy regarding the question itself is that of a tapping your finger on the calm surface of a swimming pool. You can generate a train of waves with a large wavelength, even though your fingertip is very small by comparison. In this case the frequency of the pulses determines the 'wavelength', not the size of the object doing the pulsing.

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#40
In reply to #39

Re: Set the Tone (July 2012)

07/04/2012 1:47 PM

Tapping finger will produce a tiny wave, but do a "cannonball' into that same pool if you really want to see a wave!

The point is, you can produce bas from a tiny speaker, but it takes a big driver to produce bass of any amplitude simply because the volume of air moved or compressed by a larger "piston" is both easier and lower in distortion components.

Larger drivers also "couple" better to the room.

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#41
In reply to #40

Re: Set the Tone (July 2012)

07/04/2012 3:02 PM

Agreed. Which is why 'poorly' was my initial response.(#1)

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#43
In reply to #39

Re: Set the Tone (July 2012)

07/04/2012 3:37 PM

It's instructive to look at the way the amplitude decays with distance away from your finger. Things behave differently when the radius of curvature is small compared with the wavelength.

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#4

Re: Set the Tone (July 2012)

07/01/2012 9:52 PM

The bass tones are inferred by using the high frequency harmonics of the lower frequency notes.....

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#9
In reply to #4

Re: Set the Tone (July 2012)

07/02/2012 4:53 AM

GA

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#36
In reply to #4

Re: Set the Tone (July 2012)

07/04/2012 12:43 AM

this is distortion

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#5

Re: Set the Tone (July 2012)

07/01/2012 10:56 PM

The small speakers are very inefficient in reproducing bass note for the reason you state(very bad impedance match). They boost the bass to partially compensate and we are used to it and it is tolerated.

If you ever hear sound with a large folded horn that has higher efficiency as well as larger aperture, you usually adjust the bass level to suit

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#6

Re: Set the Tone (July 2012)

07/01/2012 11:42 PM

One could design a speaker to reproduce 2Hz with a driver the size of the head of a pin.

The challenge does not ask about wave amplitude or driver voice coil power handling capabilities.

And, to explore the other end of the discussion, might we ask how the high frequencies are reproduced when the driver (not necessarily in a cell phone) is many times larger than the wavelength of the note?

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#7

Re: Set the Tone (July 2012)

07/02/2012 12:11 AM

Poorly phrased question that doesn't makes sense. Speakers aren't antennas.

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#17
In reply to #7

Re: Set the Tone (July 2012)

07/03/2012 9:37 AM

Sounds like you don't understand anything about acoustics...there are a number of similarities between acoustics and EM & antennae, if only because we use wave theory to describe both pressure waves and EM waves*.

The question does make sense.

*At least some of the time anyway....

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#46
In reply to #7

Re: Set the Tone (July 2012)

07/25/2012 1:05 AM

every wire, short or long, works as antenna

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#8

Re: Set the Tone (July 2012)

07/02/2012 1:54 AM

modulate an ultrasonic carrier?

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#10

Re: Set the Tone (July 2012)

07/02/2012 5:41 AM

The size of the speaker compared to the sound wavelength determines how directional the sound output will be. Cell phones are generally used with the speaker close to the ear, so that the lower frequencies are not attenuated as much as they would be farther from the speaker.

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#13
In reply to #10

Re: Set the Tone (July 2012)

07/02/2012 12:09 PM

Actually, it isn't the transducer size, but the baffle's size it is mounted to that determines the "directivity".

The formula to calculate the point in frequency is f3 = 115 / W, where W = width of the baffle.

Below the frequency of f3 the output will drop about 6 dB in attenuation as the transducer transitions from half-space (or 2pi, where the transducer is radiating only in the forward direction) into full-space (4pi).

Below f3 the sound actually folds or wraps around the baffle edges. The physics is a little complex, but a portion of the wave energy bends around the edge.

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#11

Re: Set the Tone (July 2012)

07/02/2012 11:02 AM

The answer to your question is "They Don't" I played Motzart's four horn concerto on my stereo system which has 15.5" woofers and on my cell phone which has a 1.2" speaker and found that the bass from the cell phone was not a true bass. The mid range was also partially missing.

Have you had your hearing checked?

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#12

Re: Set the Tone (July 2012)

07/02/2012 11:51 AM

Simple. When the excitation frequency wavelength is larger than the radius of the transducer the transducer operates in what is know as "piston mode".

It is pretty much as it sounds, the transducer cone is stroking like a piston and the compression and rarefaction occur when the transducer cone moves forward and backward.

At higher frequencies the cone vibrates much like a string and flexes or ripples.

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#14

Re: Set the Tone (July 2012)

07/02/2012 12:15 PM

My ears pick up bass notes quite well. I haven't taken time to measure then recently but i do know they do not comprise of 15 inch cones to pick up the low frequency stuff. I'm also pretty certain they do not move in and out off my head by half an inch.

Could there be a similar technology employed.

There is an old saying size doesn't matter and maybe it doesn't!

Totally agree with one of the early posters - they do do it quite badly.

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#15
In reply to #14

Re: Set the Tone (July 2012)

07/02/2012 12:23 PM

It's all about sound pressure. The smaller the transducer diaphragm, the longer the stroke required to move the same volume of air. Obviously, 1" diameter transducer can not replicate a 15" transducer for total volume of air moved.

Since the electrical energy applied to the transducer is the same as it would be for a full-sized speaker, the smaller transducer's low frequency response drops rapidly.

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#16

Re: Set the Tone (July 2012)

07/03/2012 9:30 AM

The question says mobile 'phones. Unlike speakers in free space, when held against the ear they are (effectively) driving into a restricted volume, so the problem of wavelength largely vanished.

Nevertheless, they do not in practice reproduce low tones - this is because the resonance frequency of the transducer is rather high (probably for reasons of robustness). So you have to rely on the response of the human auditory system (sensing the difference frequency as described by solar eagle and others).

The low frequency response of relatively small speakers (whether infinite baffle, resonant, or open baffle) is an entirely different matter.

I'll have to stay away again for a while...

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#18
In reply to #16

Re: Set the Tone (July 2012)

07/03/2012 10:26 AM

this would explain why headphones in the ears sound good whilst laid on the desk just sound tinny and horrible. Also explains the second hand sound the younger generation feel we should be subjected to is all higher frequency stuff. (and rubbish)

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#20
In reply to #18

Re: Set the Tone (July 2012)

07/03/2012 12:53 PM

Couldn't quite stay away...

I don't think "feel we should" has any bearing - the listener either doesn't realise that (s)he's causing noise pollution - or doesn't care.

Of course, for the listener the low frequency cut-off of even halfway decent headphones is pretty low, and the voluntary listener will hear the music(?) approximately as intended. But the overhearer will find that wavelengths that are larger than about half of the transducer dimension progressively attenuated.

As portable headphones typically have transducer dimensions less than 5-mm, this means that the slope will cover the entire audible frequency range...

The position with high-quality unsealed headphones lying on the desk is both better and worse...

Better, for two reasons -
the transducer dimensions are typically larger, and
the motion is not constrained by driving into a small-volume cavity.

Worse, because the sound from the two sides of the transducer will interfere destructively at lower frequencies.

BTW, the power density in a plane wave is proportional to the square of the peak pressure (and equally of the peak velocity). So, even for a large transducer, the displacement at constant power is inversely proportional to frequency.

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#47
In reply to #20

Re: Set the Tone (July 2012)

11/01/2012 4:24 PM

"I don't think "feel we should" has any bearing - the listener either doesn't realise that (s)he's causing noise pollution - or doesn't care"

Oh, no, no no. I used to install high power autosound systems and I can tell you for certain their goal is to be as absolutely intrusive as physically possible within the reach of their financial means. In other words they WANT everyone to hear it.

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#37
In reply to #18

Re: Set the Tone (July 2012)

07/04/2012 12:48 AM

to sound a huge volume requires more power than to sound a tiny volume!

the frequencie is not effected by the size of the soundbox, the loudness of a tone is only effected by the power of the source!

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#27
In reply to #16

Re: Set the Tone (July 2012)

07/03/2012 2:03 PM

I should have mentioned that, when used for telephony, the transmission frequency range for 'phones used to cut off below 300-Hz (so no true 'bass' there at all). Any perception of base tones was entirely due to auditory perception of difference tones.

However, AMR-WB coding has been specified since 3GPP, and this provides signals down to 50Hz.

And yes, with some phones this 50Hz is perfectly audible when the phone is held to the ear.

Still not managing quite to stay away...

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#19

Re: Set the Tone (July 2012)

07/03/2012 12:02 PM

To answer the question in the most simple terms....

They Don't.

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#21
In reply to #19

Re: Set the Tone (July 2012)

07/03/2012 12:59 PM

They do reproduce some bass tones - just not the lowest ones.

Thus, the question "how?" remains valid, and your claim to have answered it isn't.

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#22
In reply to #21

Re: Set the Tone (July 2012)

07/03/2012 1:14 PM

You show me an ear bud that can produce a 20hz sound wave and I'll recant! LOL

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#24
In reply to #22

Re: Set the Tone (July 2012)

07/03/2012 1:43 PM

Clearly you have re-written the question to conform with your answer (this probably won't make you LOL).

"Bass tones" typically start around middle C (~260Hz) (bassed on design of bass boost controls - the bass voice range extends well above this...)

Actually, the acoustic transducers in both mobile phones (the question) and ear buds (your second modification) can produce 20Hz - and placed in-or-by the ear this could even be at an audible levels. However, there are all sorts of reasons that the signal processing in the mobile phone shouldn't generate enough below even (say) 50-Hz to be audible.

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#25
In reply to #22

Re: Set the Tone (July 2012)

07/03/2012 1:46 PM

Okay, Philips model SHE2641/27 has a response from 12 hZ to 22 Hz.

You can easily get those types of responses from earbuds because the volume of air that is required to be moved is very, very small compared to even a small room.

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#26
In reply to #25

Re: Set the Tone (July 2012)

07/03/2012 1:48 PM

You mean 12Hz - 22kHz?

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#29
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Re: Set the Tone (July 2012)

07/03/2012 2:09 PM

Yes. Thanks for the catch.

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#30
In reply to #29

Re: Set the Tone (July 2012)

07/03/2012 4:20 PM

Yep, that is what I said, thanks for "teching" it up Anon, you're my "hero" ! Sorry folks, sometimes I am too simple minded and direct.

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#31
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Re: Set the Tone (July 2012)

07/03/2012 4:22 PM

Added fun for those who like experiments. Pick up a sound pressure meter, hold it in front of a cell phone on full blast and watch the result.

Does anyone else remember how bad the original Sony Walkman sounded?

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#23

Re: Set the Tone (July 2012)

07/03/2012 1:33 PM

ok so wavelength of bass notes is small as in hz, now hz is how many times a sine wave crosses a point in 1 second. so all a small speaker has to do to create lets say a 10 hz bass note is move only 10 times that second. the size actually doesn't matter. now in practical application a 1" speaker cannot possibly move as much air as lets say a 1' speaker so we come up with a decibel difference. now in real life there's 3 common kinds of "drivers" (thats the technical term for the actual part making the sound) piezoelectric, standard cone (like in your car) and armature. all three work in similar principle. you send a carrier signal, usually something like 12vdc down the wire at low amperage and then send your sound information over that, at the speaker itself the carrier signal is filtered back out. now most speakers are manufactured with additional filters, and labeled such as woofers ( filtered to produce better low frequency tones) or tweeters (filtered for higher frequency tones). resonance boxes and baffles are added to speakers because the speaker produces sound in two directions. the sound that comes out of the speaker is what you think of as the sound of the speaker, but as the speakers membrane moves back to a resting position it creates a "negative" of the sound. resonance boxes and baffles reshape and redirect the "negative" so that it is combined with the initial sound. baffling and resonance chambers are mainly for shaping the sounds propagation.

now back to the point. cell phone speakers (often piezoelectric) are filtered to give the best quality at about the normal vocal range of humans (70-7000hz) which means that depending on the speaker's specific tolerances anything lower or higher than that hz range would be degraded. thats why cell phone speakers suck for bass.

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#28
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Re: Set the Tone (July 2012)

07/03/2012 2:08 PM

Well, I have some disagreement with your description.

First, there is not a DC offset (carrier) present at the output of the amplifier. It is pure AC.

Second, even cutting off the lower end of the signal is not the primary reason that cell phone speakers lack bass. The cause has to do with sound pressure level and the amount of displacement required to produce it at a given frequency.

Essentially, the tiny speakers can not move enough volume of air to produce the low frequency sound pressure level (SPL) required to match the SPL possible at much higher frequencies.

As an example, take a signal generator and watch a large woofer as you introduce a constant voltage AC signal. As you sweep from 20 Hz upward the cone excursion (the positive and negative displacement) will drop logarithmically with frequency. Even though the amount of power remains constant over the frequency range, the displacement does not.

This is why a tiny tweeter can produce 100 dB SPL at 5 kHz while a much larger diameter woofer will be visibly moving a significant distance at 20 Hz at 100 dB.

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#32
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Re: Set the Tone (July 2012)

07/03/2012 4:55 PM

First, there is not a DC offset (carrier) present at the output of the amplifier. It is pure AC.

Depends entirely on the design of the circuit. Unless a decoupling method (capacitor or transformer), there is always some dc level, especially if you are wanting to be in the linear portion of a device.

Otherwise, yours is a good explaination.

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#34
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Re: Set the Tone (July 2012)

07/03/2012 7:01 PM

Show me one audio amplifier that has a DC voltage on its output.

If true, it would never work with any of the existing speaker systems out there because there is never a capacitor inline with a woofer. Passive crossovers would have a coil and/or resistor as part of the low pass filter.

Also, when you consider the RMS AC power required to drive an 8Ω load to 50 Watts you have an AC voltage of 20 VAC RMS. 100 Watts would require 80 VAC. Any DC bias would need to be greater than that just to prevent clipping.

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#38
In reply to #28

Re: Set the Tone (July 2012)

07/04/2012 12:56 AM

technical details - not interesting at this point!

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#33

Re: Set the Tone (July 2012)

07/03/2012 6:32 PM

With a combination of technology tricks including bigger stroke to diameter ratio, horn-like loading, dsp controlled low side gain curve, that sharply boosts gain at frequency vs sensitivity low turn point AND resonance points, something that gives to most people the feeling of an acceptable (not good) low frequency response, and this with reasonable power needs. Still, it may sound "good" or more correctly "pleasant", but the real harmonic distortion is unbelievable. S.M.

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#35

Re: Set the Tone (July 2012)

07/03/2012 7:42 PM

When a stereo was turned up loud I noticed the woofers would travel about an inch. When a friend of mine was playing his upright bass vigorously I noticed the backboard would travel about an inch.

I have a set of Bose bookshelf speakers and a Bose amplifier. They are design to make cheap equipment sound better by boosting the bass. When used them together I had to dial the bass all the way back or it was just too much. Then I plugged my Ipod into the phono input which also enhanced the bass and I couldn't dial it back enough. The problem was solved by using the line input.

One time in electronics class I picked up a 2" speaker and cupped it in my hands and it sounded real good. I wanted to make a speaker enclosure that would look like a pair of hands. I think it would have to be made out of rubber.

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#42

Re: Set the Tone (July 2012)

07/04/2012 3:08 PM

Still not quite staying away (apologies) - but here is what I believe to be a 'full and proper' answer

Historically, the answer given by Solar Eagle would have been sufficient: until 3G, the transmission system filtered out frequencies below 300-Hz, bass frequencies could only be "heard" via the autonomous auditory system 'inferring' that they should be present.

More recently, the lower limit of the transmission channel has been extended to 50Hz, and transducers have largely been modified accordingly. 50Hz is close to the G below "low C", and the more usual human bass tones are included in the range. So long as the phone is held in the usual conversational position (very close to the ear), the transducer is operating quasi into a finite volume, and low frequencies are properly audible. Low/sub-base frequencies (16-to-50-Hz still need to be 'inferred'.

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#44

Re: Set the Tone (July 2012)

07/04/2012 5:13 PM

When we set up my neighbor's TV we plugged a set of computer speakers with a subwoofer into it for better. She had bought this cabinet to set the TV on and hide all the other electronics. We placed the subwoofer inside the cabinet and got double the bass due to the cabinet resonanance.

I used to visit a friend who had an old black and white cabinet TV with a 12" speaker. I used to enjoy watching because it sounded so good. Another time I was visiting the neighbors who had a color TV with a 3" speaker. The picture may have been color but the sound was black and white.

I read about someone who had developed a circuit that made stereo sound like surround sound and that some movies used it. I've noticed some movies do sound like they are around you where others sound like they are just in front of you.

I rode with a buddy at work who had a Quad eight-track player in his van. In stereo mode it wasn't anything to get excited about. But when he hit the Quad button the sound became rich and full and was everywhere. It was like shifting into warp drive.

The most incredible sound system I ever heard was 4 Bose 901 speakers and a Phase Linear 700 watt amplifier. It would get louder, and LOUDER, AND L-O-U-D-E-R, AND....it would never sound distorted. It was always pure tone. It would get so loud it felt like the walls were turning to rubber. I've never heard anything like it before or since. The speakers in the cabinets may have been only 4", but there was 36 of them.

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#45

Re: Set the Tone (July 2012)

07/10/2012 10:17 AM

The speaker voice coils themselves are mfg'd & designed to simulate a set pattern of EQ... Which will naturally shape the wave length to push its voice coil just far enough to make an attempt to reproduce the sound but not drop bottom and ruin your speaker...

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#48

Re: Set the Tone (July 2012)

11/01/2012 7:04 PM

I must say, the 'answer' given is absolute popycock! This has absolutely nothing whatsoever to do with linear/non-linear response. It also has nothing to do with the brain reconstructing fundamentals from the harmonics. The reason a tiny speaker can reproduce bass frequencies is because it has the ability to move air at that frequency. The VOLUME (SPL) of the bass tones produced is entirely dependant on two things - distance moved and piston area. Small speakers simply produce SMALL amounts of bass frequencies. The reason we hear those tiny levels is because of an effect known as 'cabin gain' or compartment gain. When the small speaker (say, an earbud) is pressed to the ear canal it creates a sealed compartment. Break that seal a little and the bass response of your earbud drops considerably. The same effect can be demonstrated with a sealed box and an SPL meter. Place an infinite baffle speaker in a large room and take a reading from one meter at 50 hz @1W. Now enlclose the speaker in a box thats two cubic meters in volume and take the same reading with the same frequency and power and you will see about 10-15 dB of gain. Same exact thing happens when the tiny speaker is pressed up to the ear canal, but its even more pronounced due to the extremely small volume of the 'compartment'.

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