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Question:

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

4

3

1

2

Solution:

p1=p0sin2π(v-1)t
p2=p0sin2π(v)t
p3=p0sin2π(v+1)t
p=p1+p3+p2=p0sin2π(v-1)t+p0sin2π(v+1)t+p0sin2πvt
=2p0sin2πvtcos2πt+p0sin2πvt
=p0sin2πvt[2cosπt+1]