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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

1. 4 beats per second with intensity ratio 25 : 16 between waxing and waning.
2. 5 beats per second with intensity ratio 25 : 16 between waxing and waning.
3. 3 beats per second with intensity ratio 81 : 1 between waxing and waning.
4. 4 beats per second with intensity ratio 81 : 1 between waxing and waning.

Correct answer: 4 beats per second with intensity ratio 25 : 16 between waxing and waning.

Solution

The beat frequency is the difference in frequencies of the two waves: f₁ = 300 Hz and f₂ = 304 Hz, so beat frequency = |f₂ - f₁| = 4 Hz. The intensity ratio between waxing and waning is given by (A₁ + A₂)² : (A₁ - A₂)² = (4 + 5)² : (4 - 5)² = 81 : 1. Thus, the correct answer is 4 beats per second with intensity ratio 25 : 16.

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