Question

A sound wave of frequency 500 Hz in air enters from a region of temperature 25C to a region of temperature 5C. Calculate the percent fractional change in wavelength?

Answer 1

If the initial and final velocities of sound at `25^@C or 298K and 5^@C or 278K` be respectively represented by `V_i and V_f`, then we can write

`V_i/V_f=sqrt(298/278)`
since velocity of sound in air is proportional to square root of absolute temperature. The frequency remains unchanged. Here it is `nu=500Hz`

If the corresponding wavelengths are `lambda_i and lambda_f`

Then `V_i=500lambda_i and V_f=500lambda_f`

So we have

`lambda_i/lambda_f=sqrt(298/278)`

So percent fractional change in wave length

`=(lambda_i-lambdaf)/lamda_ixx100=(sqrt298-sqrt278)/sqrt298xx100`

`=(1-sqrt(278/298))xx100~~3.4%`