Two waves form 10 beats in 3 s in a gas. The wavelengths are 1 m and 1 . 0 1 m , respectively . Find out the velocity of sound in the gas .

Explanation

Let V be the belocity of sound in the gas.
As 10 beats are formed in 3 s , the beat frequency ` = (10)/(3)` Hz .
the frequency of the 1st wave ,` n_(1) = (V)/(lambda) = (V)/(1)` Hz,
the frequency of the 2nd wave, ` n_(2) = (V)/(lambda_(2)) = (V)/(1 . 0 1)` Hz
Here, ` n_(1) gt n_(2)`
` :. n_(1) - n_(2) = (10)/(3) ` or , `(V)/(1)-(V)/(1 . 01) = (10)/(3)`
or , ` V = 336 . 7 m* s^(-1)` .