Wave Motion 4 Question 31

29. A sonometer wire under tension of 64N vibrating in its fundamental mode is in resonance with a vibrating tuning fork. The vibrating portion of the sonometer wire has a length of 10cm and mass of 1g. The vibrating tuning fork is now moved away from the vibrating wire with a constant speed and an observer standing near the sonometer hears one beat per second. Calculate the speed with which the tuning fork is moved, if the speed of sound in air is 300m/s.

(1983, 6M)

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Answer:

Correct Answer: 29. (a,b,c)

Solution:

  1. Fundamental frequency of sonometer wire,

f=v2l=T/μ2l=12×0.164×0.1103=400Hz

Given beat frequency, fb=ff=1Hz

f=399Hz Using, f=f(vv+vs) or 399=400(300300+vs)vs=0.75m/s



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