Two sound waves having displacements x₁ = 2sin (1000π t) and x₂ = 3sin (1006π t), when interfere, produce (a) 5 beats/s with maximum intensity 25 units (b) 6 beats/s with maximum intensity 16 units (c) 3 beats/s with maximum intensity 25 units (d) 1 beats/s with maximum intensity 5 units

Answer: (c). f₁ = (1000π)/(2π) = 500 Hz, f₂ = (1006π)/(2π) = 503 Hz, so 3 beats/s Maximum amplitude = 2 + 3 = 5, so Imax ∝ 5² = 25 units So the answer is (c) 3 beats/s with maximum intensity 25 units.

Two sound waves having displacements x₁ = 2sin (1000π t) and x₂ =… | MHT CET 2024 (10 May, Shift 1)

Q31MHT CET 2024 · 10 MAY · SHIFT 1Easy

Beats

Two sound waves having displacements $x_1 = 2\sin(1000\pi t)$ and $x_2 = 3\sin(1006\pi t)$ , when interfere, produce

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Answer: (c)

$f_1 = \frac{1000\pi}{2\pi} = 500\text{ Hz}$ , $f_2 = \frac{1006\pi}{2\pi} = 503\text{ Hz}$ , so 3 beats/s
Maximum amplitude $= 2 + 3 = 5$ , so $I_{max} \propto 5^2 = 25$ units
So the answer is (c) 3 beats/s with maximum intensity 25 units.

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