> Q. 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 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 – LIVE ANSWER TODAY

Q. 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 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

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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 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

Solution:

Let $f_0=$ frequency of tuning fork

Then, $f_0=frac {5}{2l}sqrt {frac {9g}{mu}} , , , , , (mu= $ mass per unit length of wire)

$, , , , , , =frac {3}{2l}sqrt {frac {Mg}{mu}} $

Solving this, we get M = 25 kg

In the first case, frequency corresponds to fifth harmonic while in the second case it corresponds to third harmonic.

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