Answer
The astronauts should tune to a frequency of 36 kHz
Work Step by Step
Note that $v = 1.2\times 10^8~m/s = 0.40~c$
We can find the frequency received $f_r$ by the astronauts:
$f_r = f_s~\sqrt{\frac{1-v/c}{1+v/c}}$
$f_r = (55~kHz)~\sqrt{\frac{1-(0.40~c)/c}{1+(0.40~c)/c}}$
$f_r = (55~kHz)~\sqrt{\frac{1-0.40}{1+0.40}}$
$f_r = (55~kHz)~\sqrt{\frac{0.60}{1.40}}$
$f_r = 36~kHz$
The astronauts should tune to a frequency of 36 kHz.
