The wavelength of two waves are 50 and 51 cm respectively. The temperature of the room is `20^(@)C`. What will be the number of beats produced per second by these waves, if the speed of sound at `0^(@)C` is 332 m/sec?

Options

A. 10
B. 14
C. 24
D. None of these

Answer

B

Explanation

The velocity of sound increases with temperature.
`:' v_(t) = v_(0) + 0.61t`
`:. v_(20) = 332 + 0.61 xx 20 = 344.2 m//s`
`:. n_(1) = (v)/(lamda_(1)) and n_(2) = (v)/(lamda_(2)) :' lamda_(2) gt lamda_(1) :. n_(1) gt n_(2)`
`:. n_(1) - n_(2) = v [(1)/(lamda_(1)) - (1)/(lamda_(2))]`
`= 344.2 [(100)/(50) - (100)/(51)]`
`= 344.2 xx 100 [(1)/(50) - (1)/(51)]`
`= 344.2 xx 100 xx (1)/(50 xx 51)`
`:.` No. of beats/s `= (688.4)/(51) div 14`