Question

A stretched uniform wire of a sonometer between two fixed knife edges, when vibrates in its second harmonic gives 1 beat per second with a vibrating tuning fork of frequency 200 Hz. Find the percentage change in the tension of the wire to be in unison with the tuning fork.

Answer 1

As we know that the frequency is related to tension is

$f=\sqrt{\frac{T}{\mu }}f\propto \sqrt{T}T=K{f}^2$

taking log on both side and different latina

$\frac{DT}{T}\times 100=\frac{2\times 1}{200}\times 100\frac{DT}{T}\times 100=1$

$2$times percentage change in frequency which is $0.5$percent

So percentage change in tension$=1$percent.