First slide

Beats

Question

Two waves of lengths 50 cm and 51 cm produced 12 beats per second. The velocity of sound is

Moderate

A

306 m/s
B

331 m/s
C

340 m/s
D

360 m/s

Solution

$n_{1} = \frac{v}{λ_{1}} = \frac{v}{0 .50} and n_{2} = \frac{v}{λ_{2}} = \frac{v}{0 .51}$
$Δn = n_{1} - n_{2} = v [\frac{1}{0 .05} - \frac{1}{0 .51}] = 12$
$\Rightarrow v = \frac{12 \times 0 .51 \times 0 .50}{0 .01} = 306 m / s$

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