Wave motionHard
Question
A sonometer wire resonates with a given tuning fork forming standing waves with 5 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 position of the bridges. The value of M is:-
Options
A.25 kg
B.5 kg
C.12.5 kg
D.
kg
kgSolution
n = 
Also number of loops = Numbers of antinodes.
Hence, with 5 antinodes and hanging mass of
9 kg we have P = 5 and T = 9g ⇒ n1 =
with 3 antinodes and hanging mass M we have p = 3 and T = mg
⇒ n2 =
∵ n1 = n2 ⇒
⇒ M = 25 kg
Also number of loops = Numbers of antinodes.
Hence, with 5 antinodes and hanging mass of
9 kg we have P = 5 and T = 9g ⇒ n1 =
with 3 antinodes and hanging mass M we have p = 3 and T = mg
⇒ n2 =
∵ n1 = n2 ⇒
⇒ M = 25 kg
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