# Transverse Doppler effect of sound?

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## Main Question or Discussion Point

I have been trying to find an per reviewed article where it is actually tested that sound does not have a transverse Doppler effect. I figure that its probably do to my lack of resources. if it is could somebody give me a link to the article i would appreciate it. If not, i must ask why has it not been tested?

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Orodruin
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It is a rather trivial piece of mathematics to generalise the usual Doppler formula to a source/detector moving in an arbitrary direction. It is not very different from the usual derivation.

It is also very inuitive. If the frequency from a source moving towards you increases and from a source moving away from you decreases, you must somewhere get a zero effecr when you rotate the source velocity.

Ibix
I have never looked for such a thing. Since there is no theory that expects transverse Doppler for sound, as far as I am aware (the speed of sound being so low that relativistic effects will be utterly swamped by noise), I would be surprised to find any direct test. Without a theory predicting a transverse Doppler how would you know how precise your measurements would need to be to rule it in or out?

Theoretical considerations aside, given that Doppler sonar is a fairly well developed technology I suspect that any deviation from "no transverse Doppler" is pretty tightly constrained. I'd start by looking into Doppler sonar publications if I thought this was worth investigating.

Dale
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I have been trying to find an per reviewed article where it is actually tested that sound does not have a transverse Doppler effect. I figure that its probably do to my lack of resources. if it is could somebody give me a link to the article i would appreciate it. If not, i must ask why has it not been tested?
This isn't peer reviewed, but it is my favorite online reference for the Doppler effect in both sound and light. It does a good job of showing how the same equations apply for both. You can use this to calculate the magnitude of the transverse Doppler effect for sound.

http://mathpages.com/rr/s2-04/2-04.htm

Testing that something does not happen (at all) is tricky. You can always say that it is below your experimental sensitivity.
But the people using ultrasound Doppler to measure and visualize blood flow know very well that the effect becomes "zero" when the flow is perpendicular to the line of sight.
You can find papers if you look up "Transverse Doppler ultrasound".
In this one, for example:
http://www.jultrasoundmed.org/content/12/9/497.abstract [Broken]

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It is a rather trivial piece of mathematics to generalise the usual Doppler formula to a source/detector moving in an arbitrary direction. It is not very different from the usual derivation.

It is also very intuitive. If the frequency from a source moving towards you increases and from a source moving away from you decreases, you must somewhere get a zero effect when you rotate the source velocity.
As intuitive and trivial as it may be i would feel much more comfortable about educating people that the transverse doppler effect does not exist for sound if there were experimental proof, rather than relying on intuition.

I have never looked for such a thing. Since there is no theory that expects transverse Doppler for sound, as far as I am aware (the speed of sound being so low that relativistic effects will be utterly swamped by noise), I would be surprised to find any direct test. Without a theory predicting a transverse Doppler how would you know how precise your measurements would need to be to rule it in or out?
I do not know. I probably wouldn't of ask the question if i did. I figure that your main concern is where did you get this question without having a supporting theory. I was wondering if the transverse Doppler effect was a property of all waves. When light was first classified as a wave it was because of its wavelike properties. To me then It would seem proper that if we see any effect that involves light to test it against a different wave type "like sound" to see if it produces the same effect, rather than relying on intuition or waiting for a theory.

This isn't peer reviewed, but it is my favorite online reference for the Doppler effect in both sound and light. It does a good job of showing how the same equations apply for both. You can use this to calculate the magnitude of the transverse Doppler effect for sound.

http://mathpages.com/rr/s2-04/2-04.htm
Thank you, that was very interesting i will need to read through it a couple more times though. if i understood it correctly i should be able to measure the transverse doppler effect of sound at speeds less than the speed of sound? But to calculate it I would have to set the value of c to the speed of sound.

Dale
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Thank you, that was very interesting i will need to read through it a couple more times though. if i understood it correctly i should be able to measure the transverse doppler effect of sound at speeds less than the speed of sound? But to calculate it I would have to set the value of c to the speed of sound.
No, the value of c is 299792458 m/s. In this paper's notation you would set $c_s$ to the speed of sound, or about 340 m/s.

Ibix
Dale's link says what my parenthetical aside says - transverse Doppler comes from relativistic effects, so it will be unmeasurably small for anything moving below the speed of sound (which is about 0.000001c). If the source is moving above the speed of sound you won't have a well-defined Doppler effect to measure.

You need to set $c_s$ to the speed of sound and $c$ to the speed of light.

Dale
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Dale's link says what my parenthetical aside says - transverse Doppler comes from relativistic effects, so it will be unmeasurably small for anything moving below the speed of sound (which is about 0.000001c).
Yes, exactly. And nasu also mentioned the same thing.

You need to set $c_s$ to the speed of sound and $c$ to the speed of light.
Ok, i knew i was missing something i was reading $c$ as $c_s$

Thanks