Question

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

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

Answer 1

The correct option is A $25kg$

Frequency of vibration of vibration of string, $n=\frac{p}{2l}\sqrt{\frac{T}{m}}$

No. of loops = No. of antinodes

For, $p=5$

$T=9g$

$\therefore n_1=\frac{5}{2l}\sqrt{\frac{9g}{m}}$

For, $p=3$

$T=Mg$

$\therefore n_2=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$

$n_1{n}_2$

$\therefore \frac{5}{2l}\sqrt{\frac{9g}{M}}$ $=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$

$\Rightarrow M=25kg$