A bat is flying toward a cave wall at $27\mathrm{.}0$ m$/$s$.$What is the frequency of the reflected sound that it hears, assuming it emits sound at $52\mathrm{.}0$ kHz$?$The speed of sound is $341\mathrm{.}5$ m$/$s$.$

Hint, this problem might be a bit tricky.$$You will need to divide this problem over two steps.$$First the source $($bat$)$ is moving towards an observer $($the wall$).$Calculate the frequency that the stationary wall would observe.

Next use this frequency and the wall as a source emitting this frequency $($when the frequency is reflected back$).$The wall would be a stationary source and the bat would become an observer moving towards the source.$$Find the final frequency.