Question

The wave speed on a string is 138 m/s when the tension is 85 N. What tension will give a speed of 180 m/s?

Answer 1

Wave speed is given by the relation,

$v=\sqrt{\frac{T}{\mu }}$

where, $\mu$ is mass per unit length of the string.

Thus, from first condition,

$\mu =\frac{T}{v^{2}}=\frac{85}{138^{2}}=0.004463kg/m$

Applying it in second condition, we have

$180=\sqrt{\frac{T}{0.004463}}$

$\Rightarrow T=144.6N$