First slide

Stationary waves

Question

A sonometer wire resonates with a given tuning fork forming standing waves with five 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, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is

Difficult

A

25 kg
B

5 kg
C

12.5 kg
D

1/25 kg

Solution

The frequency of vibration of a string $n = \frac{p}{2 l} \sqrt{\frac{T}{m}}$
Also number of loops = Number of antinodes.
Hence, with 5 antinodes and hanging mass of 9 kg.
We have p = 5 and T = 9g $\Rightarrow n_{1} = \frac{5}{2 l} \sqrt{\frac{9 g}{m}}$
With 3 antinodes and hanging mass M
We have p = 3 and T = Mg $\Rightarrow n_{2} = \frac{3}{2 l} \sqrt{\frac{Mg}{m}}$
$∵ n_{1} = n_{2} \Rightarrow \frac{5}{2 l} \sqrt{\frac{9 g}{m}} = \frac{3}{2 l} \sqrt{\frac{Mg}{m}} \Rightarrow M = 25 kg$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App