Question

Find vilocity of sound in a gas when the 2 waves of wavelenth 0.8 and 0.81 metre produce 4 beat per second

Answer 1

The beat frequency (4 beat per second = 4 Hz ) corresponds to the difference between the frequencies of the two waves:

`4 Hz = f_1 - f_2` (1)

The frequency of the first wave can be written as

`f_1= (v)/(\lambda_1)`
where v is the speed of sound in the gas and
`\lambda_1 = 0.8 m` is the wavelength of the first wave, while the frequency of the second wave is

`f_2 = (v)/(\lambda_2)`
where
`\lambda_2=0.81 m` is the wavelength of the second wave. If we substitute into the first equation (1), we find

`4 Hz = (v)/(\lambda_1)- (v)/(\lambda_2) = v ((1)/(\lambda_2)- (1)/(\lambda_2) )`

and if we re-arrange it, we can find the velocity of the sound in the gas:

`v= (4 Hz)/( (1)/(\lambda_1)- (1)/(\lambda_2) )= (4 Hz)/( (1)/(0.8 m) - (1)/(0.81 m) )=259.2 m/s`