Physics - Wave on String Question with Solution | TestHub

The frequency of a vibrating string is given by $f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

This implies $f\propto \sqrt{T}$

For small changes in tension, the fractional change in frequency is given by:

$\frac{\Delta f}{f}=\frac{1}{2}\frac{\Delta T}{T}$

Given the initial frequency $f=500$ Hz and the beat frequency $\Delta f=5$ Hz, the fractional change in frequency is:

$\frac{\Delta f}{f}=\frac{5}{500}=\frac{1}{100}$

Substituting this into the relation:

$\frac{1}{100}=\frac{1}{2}\left(\frac{x}{100}\right)$

$\frac{x}{100}=\frac{2}{100}$

$x=2$

Answer: $2$