Two sources of sound placed close to each other are emitting progressive waves

Two Sources Of Sound Placed Close To Each Other Are Physics Question

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:

Options

(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

Correct Answer:

4 beats per second with intensity ratio 81 : 1 between waxing and waning

Explanation:

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 wave.

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Topics: Waves (80)
Subject: Physics (2479)

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