Question

A string fixed at both the ends is oscillating in its $3^{rd }$ overtone. If the tension in the string is $10N,$ its mass is $1gm$ and length is $4m.$ Find the frequency (in $Hz$ )?

Answer 1

$3^{rd}$ overtone, $4^{th}$ harmonic
$T=10N$
$m=1gmL=4m$
$v=\sqrt{\frac{T}{\mu }}=200ms^{- 1}$
$4\times \frac{\lambda }{2}=4$
$\lambda =2m$
$n=\frac{200}{2}=100Hz$