1. Tardigrade
  2. Question
  3. Physics
  4. A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1: 3: 4 ?

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A sonometer wire of length $114\, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?

JEE MainJEE Main 2013Waves

Solution:

Total length of the wire, $L = 114\, cm$
$n_2: n_2 : n_3 = 1 :3 :4$
Let $L_1, L_2$ and $L_3$ be the lengths of the three
As $n\,\propto \frac{1}{L}$
$\therefore L_{1} : L_{2} : L_{3}=\frac{1}{1} : \frac{1}{3} : \frac{1}{4}=12 : 4 : 3$
$\therefore L_{1}=72\,cm\left(\frac{12}{12+4+3}\times114\right)$
$L_{2}=24\,cm\left(\frac{4}{19}\times114\right)$
and $L_{3}=18\,cm\left(\frac{3}{19}\times114\right)$
Hence the bridges should be placed at $72\, cm$ and $72 + 24 = 96\, cm$ from one end. parts