Question

A one metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops ?

Answer 1

A string of mass 40 g is attached to the tuning fork

$m=(40\times {10}^{-3})kg/m$

The fork vibrates with

$f=128Hz$

$\lambda =0.5m$

$v=f\lambda =128\times 0.5$

$=64m/s$

$v=\sqrt{\left(\frac{T}{m}\right)}$

$\Rightarrow T=v^{2}m$

$=(64{)}^2\times 40\times {10}^{-3}$

$=163.84\approx 164N$