Question

Sound propagating through air at 26 °C passes through a vertical cold front into air that is 4.2 °C. If the sound has a frequency of 2000 Hz, by what percentage does its wavelength change in crossing the boundary

Answer 1

Wavelength = speed/frequency

Since the 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). For our atmosphere, this can be approximated as:

331.3 + (0.606)*T-c (see reference)
- So at 26 degrees C it will be: 349.48 m/s
- And at 4.2degrees C it will be: 328.88 m/s

Therefore, the percentage change in the wavelength is the percentage change in the speed of sound, which is:
100* [(328.88 - 349.48) / (349.48)]
= -5.89%