Q: A sonometer wire has a length of 114 cm between two fixed ends. Where should two bridges be placed to divide the wire into three segments whose fundamental frequencies are in the ratio 1 : 3 : 4 ?

Sol: In case of a given wire under constant tension,

fundamental frequency of vibration $\large n \propto \frac{1}{l}$

$\large l_1 : l_2 : l_3 = \frac{1}{1} : \frac{1}{3} : \frac{1}{4} $

= 12: 4 : 3

l_{1} = 72 cm; l_{2} = 24 cm; l_{3} = 18 cm

First bridge is to be placed at 72 cm from one end.

Second bridge is to be placed at 72 + 24 = 96