Two waves of wavelength $λ$ and $(λ + Δ λ)$ produce 5 beats per second. If $\frac{Δ λ}{λ} = \frac{λ + Δ λ}{65}$ , find the speed of sound waves in gas in which these waves produced beats.

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335 m/s

325 m/s

334 m/s

324 m/s

answer is A.

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Detailed Solution

$\frac{Δ λ}{λ} = \frac{λ + Δ λ}{65}$

$\frac{Δ λ}{λ (λ + Δ λ)} = \frac{(λ + Δ λ) - λ}{λ (λ + Δ λ)} = \frac{1}{λ} - \frac{1}{λ + Δ λ} = \frac{1}{65}$

$f_{1} - f_{2} = 5$

$\frac{v}{λ} - \frac{v}{λ + Δ λ} = 5$

From (i) and (ii)

$\frac{5}{v} = \frac{1}{65}$ ; V = 325 m/s

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