The velocity of sound in a gas, in which two wavelengths 4 . 08 m and 4 . 16 m produce 40 beats in 12 s , will be

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TestHub · Accepted Answer

If the velocity of the sound in the medium is $v$ then, $f_{1} = \frac{v}{4.08}$ and $f_{2} = \frac{v}{4.16}$

Now beat frequency,

$f_{b} = Δ f = |f_{1} - f_{2}| = \frac{40}{12} = \frac{10}{3} Hz \Rightarrow v [\frac{1}{4.08} - \frac{1}{4.16}] = \frac{10}{3} Hz \Rightarrow 707.2 m s^{- 1}$

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