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  4. Two waves of wavelengths 50 cm and 51 cm produced 12 beats per sec. The velocity of sound is

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Q. Two waves of wavelengths $50 \,cm$ and $51 \,cm$ produced $12$ beats per sec. The velocity of sound is

JIPMERJIPMER 2013Waves

Solution:

Number of beats produced per sec.
$=v_{1}-v_{2}=\frac{v}{\lambda_{1}}-\frac{v}{\lambda_{2}} $
$12 =v\left[\frac{1}{50}-\frac{1}{51}\right] $
or, $ 12=\frac{v \times 1}{50 \times 51}$
or, $ v=12 \times 50 \times 51 \,cm / s =306 \,m / s$.