Question

A sonometer wire resonates with a given tuning fork forming standing waves with $5$ antinodes between the two bridges when a mass of $9$ kg is suspended from the wire. When this mass is replaced by a mass M, it resonates with the same tuning fork forming $3$ antinodes at the same position of bridges. The value of M is?

• A. $25$ kg
• B. $5$ kg
• C. $12.5$ kg
• D. $1/25$ kg

Answer 1

The correct option is A $25$ kg

(a) The frequency of vibration of a string $n=\frac{p}{2l}\sqrt{\frac{T}{m}}$

Also number of loops $=$ Number of antinodes.Hence, with 5 antinodes and hanging mass of 9 kg.We have $p=5$ and $T=9g\Rightarrow n_1=\frac{5}{2l}\sqrt{\frac{9g}{m}}$

With 3 antinodes and hanging mass $M$

We have $p=3$ and $T=Mg\Rightarrow n_2=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$

$\because n=n\Rightarrow \frac{5}{2l}\sqrt{\frac{9g}{m}}=\frac{3}{2l}\sqrt{\frac{Mg}{m}}\Rightarrow M=25kg$