1.

Three sound waves of equal amplitudes have frequencies (v - 1), v , (v + 1) . They surperpose to give beats. The number of beats produced per second will be :

Answer»

3
2
1
4

Solution :According to SUPERPOSITION principle y = `y_(1) + y_(2) + y_(3) `.
y = a sin 2`pi` (v - 1) t+ a sin `2 pi v t + a sin 2pi`(v+1) t.
Now a sin `2 pi (v - 1) t + a sin 2pi (v + 1) `
a `[ 2 COS 2 pit sin pi v t] `
`y = a sin 2 pi vt + 2 a cos 2 pi t sin 2 pi v t.`
`y = a (1 + 2 cos 2 pi t ) sin 2 pi v t `
= A sin `2 pi v t`
Where A = `a(1 + 2 cos 2 pi t) ` is resultant amplitude .
Since intensity `prop ("Amplitude")^(2)`
`therefore` Intensity will be maximumif cos `2pi t ` =+ 1
`rArr "" 2pi t = 0, 2pi, 4pi, 6pi,.. `etc.
`rArr "" t= 0 , `Is, 2s, 3S, .... etc.
`therefore` Time period of maximum intensity is 1 second so frequency of maximum intenstiy is 1 Hz or beat frequency is 1 Hz.
`rArr ` Choice is (c) .


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