Problem 13.31

13.31. a)
We know that frequency change due to the doppler shift is given by
$f' = f \frac{v}{(v \pm v_{s})}$
We know that the velocity of sound, v, is given by
v = 343 m/s
So, the frequency heard while the train approaches is given by
$f' = 320 \frac{343}{343 - 40}$
f' = 362.2 Hz
and when the train is receding, the frequency heard is
$f' = 320 \frac{343}{343 + 40}$
f' = 286.5 Hz
So, the total change in frequency due to the doppler shift is given by
$\Delta f = (362.2 - 286.5) Hz$
$\Delta f = 75.5 Hz$

b)
We know that
$v = f' \lambda$
so solving for the wavelength, we find
$\lambda = \frac{v}{f'}$
$\lambda = .948 m$