Question

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 $1 : 3 : 4$ ?

• A. At 36 cm and 84 cm from one end
• B. At 24 cm and 72 cm from one end
• C. At 48 cm and 96 cm from one end
• D. At 72 cm and 96 cm from one end

Answer 1

Answer: (D)

At 72 cm and 96 cm from one end

Answer 2

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