Physics
Physics
Problem
A stationary source emits sound of frequency . The sound is reflected by a large car approaching the source with a speed of . The reflected signal is received by the source and superposed with the original. What will be the beat frequency of the resulting signal in Hz? (Given that the speed of sound in air is and the car reflects the sound at the frequency it has received). [Adv. 2017]Intuitive explanation
This problem chains two Doppler shifts together: first, the moving car receives a higher frequency because it's approaching the stationary source; then it reflects that higher frequency back, and the source receives an even higher frequency because the car (now acting as a moving source) is still approaching. The beat frequency is simply the difference between this doubly-shifted reflected frequency and the original emitted frequency—so you need to apply the Doppler formula twice in succession.
Intuitive explanation
This problem chains two Doppler shifts together: first, the moving car receives a higher frequency because it's approaching the stationary source; then it reflects that higher frequency back, and the source receives an even higher frequency because the car (now acting as a moving source) is still approaching. The beat frequency is simply the difference between this doubly-shifted reflected frequency and the original emitted frequency—so you need to apply the Doppler formula twice in succession.