A bat emits chirping sounds of frequency 75 kHz while hunting for moths to eat. The bat flies east at 8 m/s. Assume that the speed of sound in air is 343 m/s.
(a) A deaf moth hovers in the air in front of the bat. If it could hear the bat's chirp, what frequency would it hear?
(b) What is the frequency of the reflected sound detected by the bat?
(c) The deaf moth decides to fly westward, directly toward the bat) at a speed of 1 m/s. What frequency would it hear in this case?
(d) What beat frequency would the bat hear in this case, due to superposition of the outgoing and reflected waves? (Hint: The moth is the receiver of the sound, and then becomes the source of the reflected sound, so you need a two-step calculation.)