Answer to Question #164338 in Optics for Julius

Question

 Many bats use the Doppler Effect for detecting obstacles and prey. One species sends out high

 frequency sound waves and locates the objects in front of it from an analysis of the reflected waves. If the bat flies at a steady speed of 4ms^-1, and emits waves of frequency 90.0 kHz, what is the frequency of the wave detected by the bat after reflection from a stationary obstacle directly ahead of the bat? Derive any equation for the Doppler Effect used in the calculation.

 State what could be deduced about the obstacle if a bat detected a reflected wave of frequency less than that emitted.

Answer 1

$$f_o=\frac{c}{c-v_s}f_s=\frac{340}{340-4}90000=91071\ Hz$$

$$f_o=\left(1+\frac{v}{c}\right)f_s=\left(1+\frac{4}{340}\right)91071=92.1\ kHz$$