Question

What is the speed of the sound in a perfectly rigid rod?

Answer 1

The speed of sound depends upon the density of the medium through which it is travelling .The higher the density of the medium the faster the propagation of sound. Solids have a higher density than liquids and gases, so sound travels further in solids.

Complete answer:
Sound is a longitudinal wave and needs a medium to transmit from one location to another.Sound passes through the air by compressing and rarefying it in the direction of wave motion. In other words, air molecules travel back and forth in the direction of the sound wave (causing air pockets to compress and decompress), causing them to transmit from one place to another. To put it another way, sound cannot move without the presence of a medium.

A fully rigid rod, on the other hand, has no free atoms or molecules, and all of the particles travel as a single entity. As a result, sound from the rigid body would be transmitted immediately, and the speed of sound through a rigid body would be infinite. Another way to understand this scenario is by mathematical formulation of the speed of sound, which is:
$C = \sqrt {\dfrac{E}{P}}$
Here, $C$ is speed of sound, $E$ is modulus of elasticity (ratio of stress and strain) and $\rho$ is density. Since strain is zero for a rigid body (no change in length), $E$ is infinite for a rigid body and so is the speed of sound through it.

Note: A question emerges here: what happens when sound propagates through a medium that has no constant properties? As a result, the propagation of sound in this case can be described by the motion of wavefronts, which are lines of continuous pressure that travel over time.