Two waves of lengths $50 \;cm$ and $51\; cm$ produced $12$ beats per second. The velocity of sound is .... $m/s$
AIPMT 1999, Medium
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(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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