Speed of a longitudinal wave in a solid rod (13-12)

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Question

Propagation speed of a longitudinal wave along a solid rod
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Review

The speed of longitudinal waves in a \(\textit{solid}\) is given by a different expression than Equation 13-11. If we just consider one-dimensional waves such as those that might travel the length of a solid rod, what matters is not the \(\textit{bulk}\) modulus \(B\) but rather \(\textit{Young’s modulus}\) \(Y\). We learned in Section 9-2 that Young’s modulus tells us how difficult it is to stretch or compress a piece of material along its length; those are just the kind of stresses experienced in a rod with a longitudinal wave propagating down its long axis. So \(Y\) tells us about the restoring force in this case, and the propagation speed is