Wave Motion 2 Question 19

19. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9kg 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

(2002,2M)

(a) 25kg

(b) 5kg

(c) 12.5kg

(d) 1/25kg

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Answer:

Correct Answer: 19. (a)

Solution:

  1. Let f0= frequency of tuning fork

Then, f0=52l9gμ(μ= mass per unit length of wire )

=32lMgμ

Solving this, we get M=25kg

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



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