Two person, $A$ and $B$, each holding one end of a long solid rod.
Now person $A$ pushes the rod on one end.
Question: Is it correct that the information that the rod has been pushed will travel to the other end at the speed of light whereas the actual 'push' will travel at the speed of sound in the rod?
i.e. If the rod has length $ ct $ , then will person $B$ feel the push in time $t$ or $ct/v$? ($c$ is speed at which EM waves propagates in this experiment, and $v$ is the speed of sound in the rod.)
Answer
Sound
Disturbances always travel at the speed of sound in the medium. The wave equation is usually solved with
$$ u(x,t) = U \sin \left( \omega t \pm \frac{\omega\, x}{c} \right) $$
where $c$ is the speed of sound and $f=\frac{\omega}{2\pi}$ is the frequency of the disturbance.
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