What is the velocity of sound in a perfectly rigid rod? Why?

(D) The velocity of sound in a linear solid medium,such as a rod,is given by the formula $v = \sqrt{\frac{Y}{\rho}}$,where $Y$ is the Young's modulus and $\rho$ is the density of the material.
For a perfectly rigid rod,the change in length $\Delta l$ is zero for any applied stress.
Since Young's modulus is defined as $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{\Delta P}{(\Delta l / l)}$,as $\Delta l \to 0$,the value of $Y$ approaches $\infty$.
Substituting this into the velocity formula,we get $v = \sqrt{\frac{\infty}{\rho}} = \infty$.
Therefore,the velocity of sound in a perfectly rigid rod is infinite.