Question

A sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same, by what factor will the frequency change?

Answer 1

Wire is stretched, so frequency of stretched wire is,

\(v=\frac{n}{2L}\sqrt{\frac{T}{m}}\)

Mass per unit length

m = \(\frac{Mass}{Length}\) = \(\frac{\pi r^2lρ}{l}\) 

or m =πr²ρ

 or \(v=\frac{n}{2l}\sqrt{\frac{T}{\pi r^2ρ}}\)

or \(v \propto \sqrt{\frac{1}{r^2}}\propto n\)

\(v\propto \frac{1}{r}\propto n\)

So,frequency of sitar reduced by \(\frac{1}{3}\)rd of it’s previous value.