Answer
When the sound waves are reflected back to the source, the frequency is $~~2160~Hz$
Work Step by Step
In part (a), we found that the frequency at the detector was $1584~Hz$.
In this case:
$f = 1584~Hz$
$v_D = 29.9~m/s$
$v_S = 65.8~m/s$
We can find the frequency when the sound waves are reflected back to the source:
$f' = f~\frac{v+v_D}{v-v_S}$
$f' = (1584~Hz)~(\frac{329~m/s+29.9~m/s}{329~m/s-65.8~m/s})$
$f' = 2160~Hz$
When the sound waves are reflected back to the source, the frequency is $~~2160~Hz$
