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So a person stands at a far distance from an audio device. The audio device emits a sound and the person wants to get the exact time. He knows about speed of sound and has a meter stick to measure his distance between himself and the audio device. What set of measurements can help him determine the time the beep is emitted. He also has a clock.

The way I approached this question was to get a length b/t the man and the beeper. Once he gets the value of distance x, and the man knows the speed of sound, he can determine how long ago the beep occurred by dividing the distance of him and the audio device and the speed of sound. He also reads what time it is when the beep occurred. By doing that, he can subtract the time it took to have the sound travel to him with the time read on the clock and determine the time.

Am I completely off on this? This is an early introduction into relativity.

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  • $\begingroup$ Yep, that'll do it, assuming the man and the speaker are at rest relative to each other. It gets a bit more complicated if they have relative motion. $\endgroup$ – Brionius Apr 22 '15 at 10:53
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Yes, it's like that.

You have described the basic conception of retarded potential in acoustic radiation (which will be one of the typical relativistic topics in electromagnetism).

You have not specified the medium between the device and the listener but it actually doesn't matter. For more media you only need to specify more times and subtract them all (cause of varying speed of sound). Interesting is, that this modell actually forbids the existence of perfectly rigid bodies. The sound should move the entire body as one piece and therefore the information goes throught the body in no time - faster than speed of light.

When there is a movement of the listener or device (of constant speed $\vec{v}$) the velocity potential (only a step away of acoustic pressure) is:

$$ \Phi = \frac{1}{4\pi}\frac{q(t-\frac{R}{c_0})}{R(1-M\cos\theta)} $$

where q(t) is a source term, R the distance between the source and listener at the time of sound radiation, $\theta$ the angle between $\vec{v}$ and $\vec{c_0}$ and $M = v/c_0$ the Mach number.

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