# Hearing a sound backwards because of Doppler effect

Consider a supersonic plane (mach 2) aproaching a stationary sound source (e.g a fog horn on a boat).

If I understand it correctly, the passengers in the plane can hear the sound twice. First at a 3 times higher frequency, and then (after they passed the source) a second time at normal frequency but backwards. None of the textbooks or web sites mention this backwards sound. Yet I am quite sure it must be there.

Am I correct? And if so, is it actually observed (e.g. By fighter pilots) and why do textbooks never mention this?

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I doubt that fighter pilots can hear anything happening outside the plane (just because it's so loud), and I can't think of any other supersonic motion, so I wouldn't be surprised if this effect has never been observed. But it's an interesting question. –  David Z Sep 19 '11 at 22:38
FYI Gareth Loy's Musimatics book mentions it at pg. 230; one gets it from Doppler shift eq. $f_d=f\frac{v_s}{v_s-u}$ (in 1d), where $v_s$ is sound speed, $u$ is the emitter's relative speed and $f$ the frequency being emitted if $u>v_s$. –  eudoxos Sep 20 '11 at 9:12
i don't think this reversal of sound would take place. –  Vineet Menon Sep 21 '11 at 4:59
@Vineet Menon: fully irrelevant what you think unless you give an argument. –  eudoxos Sep 21 '11 at 18:15
@David Zaslavsky: how about moving surface wave source on water? (to be sure, I really mean surface waves, not acoustic waves; Doppler effect is the same) –  eudoxos Sep 21 '11 at 18:17

## 1 Answer

why do textbooks never mention this?

Because in order to travel at supersonic speeds, human beings must be enclosed in a rigid metal tube of some sort. Also, these metal tubes they ride in at those speeds generally tend to be insulated against noise from the outside.

As for trying to place some sort of microphone outside said metal tube, the propulsion system would risk drowning out any atmospherically transmitted noise (i.e. noise can be transmitted through the body of the structure).

Now, if you run the math, it still doesn't work quite like hearing it backwards (see the comment by eudoxos). Although you would encounter the soundwaves in "reverse" order, the shockwaves around you would disrupt anything around you as to make the notion of noise from them irrelevant.

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There are so many "Gedankenversuch" questions her, which are absolutely out of experimental reach, esp. in GR field. They are discussed without any objection. Why the effort here to prove the experimental difficulties? eudoxos gave the right answer, nothing more to say about it. –  Georg Sep 21 '11 at 11:00
I did ask why so many textbooks fail to mention it. The answer from eudoxos I knew already (or at least strongly suspected) –  Kris Van Bael Sep 21 '11 at 22:15