Two sources of sound placed close to each other

Asked by admin @ 13/08/2021 in Physics viewed by 246 People

Two sources of sound placed close to each other are emitting progressive waves given by y₁ = 4 sin 600 πt and y₂ = 5 sin 608 πt. An observer located near these two sources of sound will hear(a) 4 beats per second with intensity ratio 25 : 16 between waxing and waning.(b) 8 beats per second with intensity ratio 25 : 16 between waxing and waning(c) 8 beats per second with intensity ratio 81 : 1 between waxing and waning(d) 4 beats per second with intensity ratio 81 : 1 between waxing and waning

Answered by admin @ 13/08/2021

Answer - (d) 4 beats per second with intensity ratio 81 : 1 between waxing and waning

Given, y
1 = 4 sin 600
πt and y2 = 5 sin 608
πt

Comparing with general equation

y = a sin 2π ft we will get f1 as 300Hz and f2 as 304Hz

Thus,

2πf₁ = 600π , f₁ = 300 …(1)

2πf₂ = 608π , f₂ = 304 …(2)

| f₁ – f₂ | = 4 beats

Iₘₐₓ / Iₘ.ₙ = (A₁ + A₂)² / (A₁ – A₂)²

= (5 + 4)² / (5 – 4)²

= 81/1

Where, A₁ , A₂ are amplitudes of given two sound waves.

Hence 81:1 ratio

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