First slide

Standing 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

Easy

A

25 kg
B

5 kg
C

12.5 kg
D

1 /25 kg

Solution

$v_{1} = {nλ}_{1} = \sqrt{(\frac{T_{1}}{m})} = \sqrt{(\frac{9 g}{m})} v_{2} = {nλ}_{2} = \sqrt{(\frac{T_{2}}{m})} = \sqrt{(\frac{Mg}{m})} \frac{λ_{2}}{λ_{1}} = \sqrt{(\frac{M}{9})} or \frac{5}{3} = \sqrt{(\frac{M}{9})} or M = 25 kg$

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