Answer
The bat hears a frequency of $~~41,000~Hz$
Work Step by Step
First we can find the frequency of the sound reflected off the wall.
In this situation:
$f = 39,000~Hz$
$v_D = 0$
$v_S = 0.025~v$
We can find the frequency of the sound reflected off the wall:
$f' = f~\frac{v}{v-v_S}$
$f' = (39,0000~Hz)~(\frac{v}{v-0.025~v})$
$f' = 40,000~Hz$
Then we can find the frequency that the bat hears.
In this situation:
$f = 40,000~Hz$
$v_D = 0.025~v$
$v_S = 0$
We can find the frequency that the bat hears:
$f' = f~\frac{v+v_D}{v}$
$f' = (40,000~Hz)~(\frac{v+0.025~v}{v})$
$f' = 41,000~Hz$
The bat hears a frequency of $~~41,000~Hz$
