Question

A sonometer wire has a total length of $1m$ between the fixed ends. Two wooden bridges are placed below the wire at a distance $1/7m$ from one end and $4/7m$ from the other end. The three segments of the wire have their fundamental frequencies in the ratio :

• A. $1:2:3$
• B. $4:2:1$
• C. $1:\frac{1}{2}:\frac{1}{3}$
• D. $1:1:1$

Answer 1

The correct option is B $4:2:1$

The three segments of the wire have length ratio $1:2:4$.
Fundamental frequency of a sonometer is inversely proportional to it's length.
So, the three segments of the wire have their fundamental frequencies in the ratio $4:2:1.$