Two sound waves with wavelengths `5.0 m` and `5.5 m` respectively, each propagates in a gas with velocity `30m//s` We expect the following number of beats per second:

Options

A. `12`
B. 0`
C. `1`
D. `6`

Answer

D

Explanation

Let `lamda_1=5.0m,v=330m//s` and `lamda_2=5.5m` The relation between frequency, wavelength and velocity is given by
`v=nlamda`
`impliesn=(v)/(lamda)` ..(i)
The frequency corresponding to wavelength `lamda_1`,
`n_1=(v)/(lamda_1)=(330)/(5.0)=60Hz`
The frequency corresponding to wavelength `lamda_2`,
`n_2=(v)/(lamda_2)=(330)/(5.5)=60Hz`
Hence no of beats per second
`=n_1-n_2=66-60=6`