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.