Chapter 20: Problem 75

Question: A $\nu_0~=~2000~{\rm Hz}$ siren and a civil defense official are both at rest with respect to the earth. What frequency does the official hear if the wind is blowing at $v~=~12~{\rm m/s}$ from (a) the source to the observer, and (b) from the observer to the source?

Solution: To see what is happening here, we should move to the rest frame of the atmosphere, and in which case both the observer and siren are moving at $v~=~12~{\rm m/s}$ in the same direction. It is clear then that the freq. heard by the official is

$$\nu_1 = \nu_0 \left({c+v\over c+v}\right) = \nu_0 = 2000 \ {\rm Hz} \ \ \ ,$$ (16)

in both cases!