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# Metal Rod - Length of Sound Wave?

02/28/2010 12:50 PM

What will be the length of the sound wave with a frequency of 28 kHz running a metal rod made of alloy steel, on which the wound coil of the stimulant transformer.

What is the speed of sound in such a metal mentioned above ?

How to correctly calculate such a set?

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Guru

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#1

### Re: What will be the length of the sound wave in metal rod

02/28/2010 1:11 PM

Simple calculation. Simply find the propagation velocity of the alloy in question expressed in units per second, and divide by the frequency.

For example, the speed of sound in air at standard temperature and pressure (STP) is 768mph, which can be expressed as 1125f/s or 343m/s. Assuming a frequency of 28KHz then, the wave length would be (343m/s)/(28,000 waves/s)=0.01225 meters, or 12.25cm.

This same equation, wl=v/f can be used to find the wave length of electromagnetic energy as well. Just be careful of your units.

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#13
In reply to #1

### Re: What will be the length of the sound wave in metal rod

03/01/2010 3:42 PM

Dr Moose

I think so - if the air has a different density than the metal the speed of sound in air is different from the speed of sound in metal and other denser centers.

By analogy - the wavelength is also different and probably much shorter.

BR

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#17
In reply to #13

### Re: What will be the length of the sound wave in metal rod

03/01/2010 4:07 PM

Absolutely true. The speed of sound in air is vastly lower than in metal, and the wavelength of a given frequency will be correspondingly shorter in the denser medium. Never the less, the specified formula will still yield the correct wavelength, all other things being equal.

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#21
In reply to #17

### Re: What will be the length of the sound wave in metal rod

03/01/2010 5:18 PM

OOPS! The wavelength of a given frequency will be longer in the denser material (metal) than in the less dense material (air).

Now if we were comparing two solids, then your statement would probably be correct, although there are other contributing factors, such as the rod diameter, as someone indicated in an earlier post.

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#23
In reply to #21

### Re: What will be the length of the sound wave in metal rod

03/01/2010 6:35 PM

You are right, of course sir. Isn't it funny how the dumb mistakes are always the ones that get us, dropping a decimal point, reversing a sign, adding 2 + 2 and getting 5?

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#24
In reply to #23

### Re: What will be the length of the sound wave in metal rod

03/01/2010 7:05 PM

Thanks for responding graciously!

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#25
In reply to #24

### Re: What will be the length of the sound wave in metal rod

03/01/2010 7:12 PM

"If you rebuke a fool, he will hate you for it, but if you rebuke a wise man, he will love you and gain knowledge from you." Proverbs 8:8-9

I try not to be a fool.

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#28
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### Re: What will be the length of the sound wave in metal rod

03/02/2010 3:14 AM

Nobody said that one of us is a fool.

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#2

### Re: What will be the length of the sound wave in metal rod

02/28/2010 1:12 PM

v=fλ.

Assuming you mean wavelength (λ)... you know frequency (f), dunno what the velocity of sound insteel alloy is, but I expect mr Google can tell you.
(I reserve the right to be confused by the Q as I don't think it makes sense, unless you mean wavelength)

Del

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#4
In reply to #2

### Re: What will be the length of the sound wave in metal rod

02/28/2010 1:46 PM

I think that it is not sound anyway. 13,330 feet/second or was it meters/second is speed in steel. I don't care enough to go back and check Wiki again for the units.

Humans can't normally hear anything above 20,000 Hz anyway.

When you get to be my age, it's down around 12,000.

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#5
In reply to #4

### Re: What will be the length of the sound wave in metal rod

02/28/2010 1:53 PM

12,000 ! Durn whipper-snappers. Old guys like me that worked in mills and factories have what audiologists call "factory ear". I'm down 75 dB by 4000 Hz.

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#26
In reply to #5

### Re: What will be the length of the sound wave in metal rod

03/01/2010 7:14 PM

Well Pappy, I have a 10KHz ring in my ears that is very annoying.

And my wife complains that I'm deaf as a rock.

This thread has turned into something I hadn't expected, and this post has strayed far into OT land. Wait a minute, . There, did you hear that?

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#27
In reply to #26

### Re: What will be the length of the sound wave in metal rod

03/01/2010 7:47 PM

The bad part is that I almost match the old Bell Telephone equipment now, but there ain't any. On the other hand, I actually hear most voices (in some sort of odd phenom, I can hear a whisper at 20 feet about as well as a normal voice at 3 feet), but I can pretend not to hear. That way, I don't have to talk with idiots that didn't have anything to say anyway.

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#6
In reply to #2

### Re: What will be the length of the sound wave in metal rod

02/28/2010 2:01 PM

Sorry, just figured out how to do the Greek alphabet on this silly thing. But yes, that is the same equation, just slightly rearranged and substituting wl (wavelength) for λ (lambda). I always try to stick to terminology that is easily understood, even if it's not always technically correct.

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#3

### Re: What will be the length of the sound wave in metal rod

02/28/2010 1:42 PM

Yes, Mr. Google led me here for the speed of sound in steel. Now do the math.

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#12
In reply to #3

### Re: What will be the length of the sound wave in metal rod

03/01/2010 3:35 PM

Yes Redfred,

thank you for your kind help.

Mr google is very useful tool, however I found it any time ago.

if I have experiment, based on calculations from the table, it appears that different speeds are for the same material. The resonance of the rod of the same length is very close to each other, but different frequencies of vibration. Thus, these data are empirical.

Anyway, all indications are valuable to me and thank all for it.

BR

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#18
In reply to #3

### Re: What will be the length of the sound wave in metal rod

03/01/2010 4:14 PM

By the way,do you know how is the approximated speed inside Titanium ?

this material is no present in the table.

tjako

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#19
In reply to #18

### Re: What will be the length of the sound wave in metal rod

03/01/2010 4:18 PM

Wikipedia specifies 5090m/s in a thin rod at room temperature.

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#7

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 12:07 AM

Sounds a lot like an electronically stimulated version of the Kundt's tube experiment...

I'm pretty sure that the actual speed of pressure waves (like some before me, I hesitate to call them sound waves, at 28kHz) will depend on the exact alloy and on the temper of the rod.

For the experiment to work well, the rod would need to be 1/2 wavelength long for the excitation frequency. Thus you would have to either change the rod length or change the excitation frequency, to obtain resonance in the rod, then adjust the air column for resonance in the air. Even though it is an ultrasonic frequency, it would probably still be wise to use ear protection while doing the experiment. If you get it to work, it should be very interesting!

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#16
In reply to #7

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 4:05 PM

Kund's tube experiment is much embarrassing in my case.

Other deductions are correct.

BR

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#20
In reply to #16

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 4:53 PM

"embarrassing"? Why? Pronounce it as close as possible to the original German, and there is no problem there.

I enjoyed the experiment myself, and so did my students, when I was teaching physics.

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#8

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 6:53 AM

If your concern is that you might unwittingly stimulate large vibrations in the rod, watch out for flexural vibrations. These will be at much lower frequency than the longitudinal ones in the rod. Also, the speed of sound in a rod will be somewhat lower than the standard number for speed in the solid material, because the thickness of a (thinnish) rod is not constrained as it would be if was larger than the wavelength.

Fyz

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#9
In reply to #8

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 6:56 AM

P.S. The lowest rod resonance could be at anywhere between 1/2 wavelength or 1/4 wavelength - depending on how you have mounted the rod.

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#14
In reply to #9

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 3:44 PM

You are right!

either the node or arrow

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#10

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 8:00 AM

If I recall correctly, the velocity of sound in any material is (modulus/density)1/2. Once you know the velocity, the calculation of wavelength is simple. Grain size will not affect velocity, but will affect Q and other damping properties.

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#11

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 8:17 AM

Homework?

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#15
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### Re: Metal Rod - Length of Sound Wave?

03/01/2010 3:55 PM

No it is not homework.

although the problem seems to be ridiculously simple, so it's not.

material that I intend to use is expensive and further experiments I no longer have the time. Therefore, hoping to help an intelligent person with this problem are in contact.

Thank you also to all who treated my inquiry seriously.

BR

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#22

### Re: Metal Rod - Length of Sound Wave?

03/01/2010 6:28 PM

The longitudinal velocity of sound in a slender steel rod is 5.05E5 cm/sec. At 28 kHz a wavelength would be 5.05E5/28E3=18.04cm or about 7.10 inches. A half wavelength transducer would be 7.10=3.55 inches. The velocity is temperature dependent, but doesn't change significantly with type of steel or heat treatment because neither elastic modulus or density are very much influenced by those parameters.

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