Question

A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz. (a) What could be the maximum value of the fundamental frequency ? (b) If transverse waves can travel on this string at a speed of $40m{s}^{-1}$, what is its length ?

Answer 1

This wire makes a resonant frequency of 240 Hz and 320 Hz.

The fundamental frequency of the wire must be the factor of 240 Hz and 320 Hz.

(a) So, the maximum value of fundamental frequency is 80 Hz.

(b) Wave speed,

v = 40 m/s

$\Rightarrow L\times 80=\left(\frac{1}{2}\right)\times 40$

$\Rightarrow L=\frac{1}{4}m=0.25m$