Question

Sound propagating through air at 35°C passes through a vertical cold front into air that is 4.6°C. If the sound has a frequency of 2480 Hz, by what percentage does its wavelength change in crossing the boundary?

Answer 1

As we know that -

Wavelength = speed/frequency

On the variation of the temperature, frequency of the sound will not change, the wavelength change will depend only on the change in the speed of sound.

The speed of sound is given by:
c = sqrt(gamma*k*T/m)
(where gamma is the adiabatic gas constant, k is Boltzmann's constant, T is absolute temperature (Kelvin), m = average molecular mass).

Now for our atmosphere, this can be approximated as:

331.3 + (0.606)*T-c (see reference)
- So at 35 degrees C, speed of sound = 352.5 m/s
- At 4.6 degrees C it will be: 334.1 m/s

So, percentage change in the wavelength is the percentage change in the speed of sound,

And this is equal to -  
100* [(334.1 - 352.5) / (352.5)] = -5.23 %