Question

The speed of a transverse wave in a wire of $1.0m{m}^2$ cross-section under a tension of 0.98 N is $1\times {10}^{x}m/s$. Find x, if density of the material of wire is $9.8\times {10}^{3}kg/m^3$.

Answer 1

Velocity of a transverse wave in a string of tension $T$ and mass per unit length $\mu$ is $\sqrt{\frac{T}{\mu }}$.

Here $\mu =\frac{m}{l}=\frac{\rho Al}{l}=\rho A$

where $\rho$ is the density of wire.

Thus $\mu ={9.8}^{\times }{10}^3\times {10}^{-6}kg{m}^{-1}$

$=9.8\times {10}^{-3}kg{m}^{-1}$

Thus speed of the wave=$\sqrt{\frac{0.98}{9.8\times {10}^{-3}}}=10m/s$