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 positions of the bridges. The value of $M$

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

Answer 1

Answer: (A)

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, $p=3$
$T=Mg$
$\therefore n_2=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$
$n_1{n}_2$
$\therefore \frac{5}{21}\sqrt{\frac{9g}{M}}=\frac{3}{21}\sqrt{\frac{Mg}{m}}$
$\Rightarrow M=25kg$