Two waves of lengths 50 ;cm and 51 ; cm produced 12 beats per sec… - Vidyadip

MCQ

Two waves of lengths $50 \;cm$ and $51\; cm$ produced $12$ beats per second. The velocity of sound is .... $m/s$

✓
$306$
B
$331$
C
$340 $
D
$360 $

✓

Answer

Correct option: A.

$306$

a
(a) ${n_1} = \frac{v}{{{\lambda _1}}} = \frac{v}{{0.50}}$ and ${n_2} = \frac{v}{{{\lambda _2}}} = \frac{v}{{0.51}}$

$\Delta n = {n_1} - {n_2} = v\,\left[ {\frac{1}{{0.05}} - \frac{1}{{0.51}}} \right] = 12$

==> $v = \frac{{12 \times 0.51 \times 0.50}}{{0.01}} = 306\,m/s$

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