Fundamental frequency of a sonometer wire is $n$. If the tension is made 3 times and; length and diameter…
Fundamental frequency of a sonometer wire is $n$. If the tension is made 3 times and; length and diameter are also increased 3 times, what is the new frequency?
$\frac{n}{3\sqrt{3}}$
$3n$
$\sqrt{3}n$
$\frac{n}{\sqrt{3}}$
Solution
Fundamental frequency,
$n = \frac{v}{2l} = \frac{\sqrt{T/\mu}}{2l} = \frac{\sqrt{T/\rho s}}{2l} = \frac{\sqrt{T/\rho \pi r^2}}{2l}$
$\therefore n \propto \frac{\sqrt{T}}{2l} \times \frac{1}{\sqrt{\rho \pi r^2}}$
Given that tension, diameter and length all are made 3 times.
$\therefore n\text{ will become }\frac{1}{3\sqrt{3}}\text{ times.}$