C$8$: Two speakers putting out the same single frequency sound are lined up $57cm$ apart. A listener is lined up with both speakers $($everything is along one dimension$)$ and the listener is $2\mathrm{.}00$ meters away from the closest speaker.

$($a$)$ Draw the situation.

$($b$)$ What is the lowest frequency tone the speakers can produce which would cause the listener to hear a loud sound due to constructive interference?

$($c$)$ What is the lowest frequency that would cause the listener to hear a very quiet sound due to destructive interference?