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 for

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 [2002]

Smart Achievers · Accepted Answer

(1)

$Fundamental frequency, f_{0} = \frac{P}{2 ℓ} \sqrt{\frac{T}{μ}}$

$= \frac{5}{2 ℓ} \sqrt{\frac{9 g}{μ}} = \frac{3}{2 ℓ} \sqrt{\frac{M g}{μ}}$

$\Rightarrow M = 25 kg$

As frequency corresponds to 5th and 3rd harmonic as $P = 5$ and $P = 3$ respectively.

Solution

1 25 kg

2 5 kg

3 12.5 kg

4 1/25 kg

Ans.
(1)

$Fundamental frequency, f_{0} = \frac{P}{2 ℓ} \sqrt{\frac{T}{μ}}$

$= \frac{5}{2 ℓ} \sqrt{\frac{9 g}{μ}} = \frac{3}{2 ℓ} \sqrt{\frac{M g}{μ}}$

$\Rightarrow M = 25 kg$

As frequency corresponds to 5th and 3rd harmonic as $P = 5$ and $P = 3$ respectively.

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