Answer
The car is moving at a speed of 114 m/s
Work Step by Step
We can write an expression for the frequency $f_a$ heard as the car approaches.
$f_a = \frac{f}{(1-\frac{v_{car}}{v_{snd}})}$
We can write an expression for the frequency $f_r$ heard as the car recedes.
$f_r = \frac{f}{(1+\frac{v_{car}}{v_{snd}})}$
Since the frequency drops by an octave, $f_a = 2f_r$. We can find the speed of the car.
$f_a = 2f_r$
$\frac{f}{(1-\frac{v_{car}}{v_{snd}})} = \frac{2f}{(1+\frac{v_{car}}{v_{snd}})}$
$1+\frac{v_{car}}{v_{snd}} = 2(1-\frac{v_{car}}{v_{snd}})$
$\frac{3~v_{car}}{v_{snd}} = 1$
$v_{car} = \frac{v_{snd}}{3}$
$v_{car} = \frac{343~m/s}{3}$
$v_{car} = 114~m/s$
The car is moving at a speed of 114 m/s.
