When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by: y₁ = 0.05cos (0.50π x - 100π t) y₂ = 0.05cos (0.46π x - 92π t) where y₁, y₂ and x are in meters and t in seconds. The speed of sound in the medium is: (a) 92 m/s (b) 200 m/s (c) 100 m/s (d) 332 m/s

Answer: (b). Wave speed v = (ω)/(k). Wave 1: v = (100π)/(0.50π) = 200 m/s Wave 2: v = (92π)/(0.46π) = 200 m/s (same medium, same speed). So the answer is (b) 200 m/s.

When two sound waves travel in the same direction in a medium, the… | JEE Main 2013 (9 Apr, Shift 1)

Q62JEE Main 2013 · 9 APR · SHIFT 1Medium

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When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by:

$y_1 = 0.05\cos(0.50\pi x - 100\pi t)$

$y_2 = 0.05\cos(0.46\pi x - 92\pi t)$

where $y_1,\ y_2$ and x are in meters and t in seconds. The speed of sound in the medium is:

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Answer: (b)

Wave speed $v = \dfrac{\omega}{k}$ .
Wave 1: $v = \dfrac{100\pi}{0.50\pi} = 200\text{ m/s}$
Wave 2: $v = \dfrac{92\pi}{0.46\pi} = 200\text{ m/s}$ (same medium, same speed).
So the answer is (b) 200 m/s.

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