Question

A sonometer wire of length 120 cm is divided into three segments of lengths in the ratio of 1:2:3. What is the ratio of their fundamental frequencies?

• A. 3:2:1
• B. 4:2:1
• C. 5:3:2
• D. 6:3:2

Answer 1

The correct option is D 6:3:2

The frequency of the fundamental mode is given by $f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$.
$\therefore f\propto \frac{1}{L}$
Hence, $f_1:f_2:f_3=\frac{1}{L_1}:\frac{1}{L_2}:\frac{1}{L_3}$
Now, $L_1=20cm,L_2=40cm,L_3=60cm$
Therefore, $f_1:f_2:f_3=\frac{1}{20}:\frac{1}{40}:\frac{1}{60}=6:3:2$
Hence, the correct choice is (d).