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Say you have a diamond pole traveling in the direction it's pointing at close to the speed of light, the back end of it gets tapped to produce a sound wave through it. Does the wave moving in the direction of travel appear different from the wave bouncing back from the front end?

Diamond because sound travels fast in diamond, the effect of any sound would be greater.

This is also from an outside stationary observer.

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If the speed of the sound is $v_s$ in the rest frame of the diamond, the speed of sound in the diamond obeys the relativistic velocity addition formula below from the viewpoint of the observer standing outside the diamond:

$$w_s=\frac{v_s\pm v}{1\pm \frac{vv_s}{c^2}}\space,$$

where $v$ is the speed of diamond in the lab frame of reference. "$+$" is for when the speed of sound is in the direction of $v$, and "$-$" is for when the sound wave bounces back.

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