Calculate the velocity off sound in a gas in which two wavelength 204 cm and 208 cm produce 20 betas in 6 sec.

Explanation

In the given case.
Wavelength of first wave `lamda_(1)=204cm`
Wavelength of the second wave `lamda_(1)=208cm`
let velocity of sound in the gas is v cm/s then frequency of first wave
`f_(1)=(v)/(lamda_(1))=(v)/(204)`
and frequency of second wave
`f_(2)=(v)/(lamda_(2))=(v)/(208)`
Beat frequency
`f=(20)/(6)=Hz`
or `f_(1)-f_(2)=(20)/(6)`
or `(v)/(204)-(v)/(208)=(20)/(6)`
or `(v[208-204])/(204xx208)=(20)/(6)`
or `v=(20)/(6)xx(204xx208)/(4)cm//s`
`=35360cm//s=354.6m//s`