Question

Hipposideros bicolor, a bat of southeast Asia, emits a constant frequency echolocation call at and around 131 kHz. To optimize their perception of echoes, they have what biologists call an "acoustic fovea" in which the bat has extreme auditory sensitivity at 131 kHz. These bats actually adjust the frequency of their calls so that their echoes return at 131 kHz. That is, they compensate for Doppler shifts as a result of their movement. (see formula sheet, next page) Consider the case of an H. bicolor flying home with a full belly after an evening out foraging. The bat performs something of a dive heading toward its roost at 20 m/s. Help this bat get homel Calculate the frequency at which the bat should call to receive echoes of its roost at 131 kHz. Note, this may be more complicated than you might at first think, but you might find an easy way to solve it if you think about mirrors.

Answer 1

"moving speed of bat = 20 m/s = v_s Loost at rest (listener) = v_L = 0 Frequency emitted by bat = theta variant_b Speed of sound in air v = 330 m/s Frequency of the sound as detected by Loost/target is given by theta variant' = (v/ v - v_s) theta variant_b Here (v_s - v_b) Target is now bat because it is producing echo and bat is now listener there the v_s = 0 and v_L is positive v_s - velocity of loost, v_L rightarrow velocity of bat = v_b v"" = (v + v_L/v) theta variant' = (v + v_b/v) times (v/v - v_b) theta variant_b given theta variant"" = 131 Hz and v = 330 m/s v = 330 m/s v_b = 20 m/s 131 = (130 + 20/330 - 20) times theta variant_b Frequency of bat = 131 Hz times 310/350 = 116 Hz theta variant_b = 116 Hz Frequency of bat"