If the speed of longitudinal waves is equal to $10$ times the speed of the transverse waves in a stretched…
If the speed of longitudinal waves is equal to $10$ times the speed of the transverse waves in a stretched wire of material which has modulus of elasticity $E$, then the stress in the wire is
$10E$
$100E$
$\frac{E}{10}$
$\frac{E}{100}$
Solution
According to the question, $\sqrt{\frac{E}{\rho}} = 10 \sqrt{\frac{T}{\mu}}$
$\Rightarrow 100 \left(\frac{T}{\mu}\right) = \frac{E}{\rho} \Rightarrow \frac{T}{s} = \frac{E \mu}{100 \rho s}$
Since, $\rho s = \mu$
$\therefore \text{Stress} = \frac{T}{s} = \frac{E}{100}$