Question

A sonometer wire, 65 cm long, is in resonance with a tuning fork of frequency n. If the length of the wire is decreased by 1 cm and it is vibrated with the same tuning fork, then 8 beats are heard per second. What is the value of n?

Answer 1

length of sonometer wire, l = 65cm

given, in resonance with a tunning fork of frequency n.

so, n = 1/2l √{T/m}

or, n = 1/2(65) √{T/m}......(1)

length of sonometer wire is decreased by 1cm so, new length, l' = 65 - 1 = 64cm

then, frequency of tunning fork is N.

now, N = 1/2l' × √{T/m}

= 1/2(64) × √{T/m} ......(2)

a/c to question,

8 beats are heard per second.

so, N - n = 8

or, N = n + 8 .....(3)

now from equations (1) , (2) and (3),

n/(n + 8) = 64/65

or, 65n = 64n + 8 × 64

or, n = 64 × 8 Hz = 512 Hz

Answer 2

Answer:

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