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Q.
A vibrator makes $150 \,cm $ of a string to vibrate in $8$ loops in the longitudinal arrangement when it is stretched by $150\, N$. The entire length of the string is then weighed and is found to weigh $400 \,mg$. Then
Solution:
$f =\frac{ P }{2 \ell} \sqrt{\frac{ T }{\mu}}$, here $P =8$
$\ell=1.50 \,m , T =150\, N$,
$\mu=\frac{ m }{\ell}=\frac{400 \times 10^{-6}}{1.50}$
$f =\frac{8}{2 \times 1.50} \sqrt{\frac{150 \times 1.50}{400 \times 10^{-6}}}$
$f =2000 \,Hz$ or $2\, kHz$