Question

A police car with its 300-Hz siren is moving toward a warehouse at 30 m/s, intending to crash through the door. The sound bounces off the warehouse door and travels back to the police officer in the moving car. Using 340 m/s as the speed of sound, what is the beat frequency the officer hears

Answer 1

Answer: The frequency heard will be f = 275.675Hz

Explanation: When an object emitting sound is moving, it occurs a phenomenon called Doppler shift or Doppler effect. What happens is that the sound gets higher when the moving object comes closer the observer and becomes lower after it passes, This change is due to the quantity of waves that passes through an area in an unit of time.

The formula to calculate the Doppler effect is as follows

f = ($\frac{c}{c+Vs}$) · f₀

f is the observed frequency;

c is the speed of sound;

Vs is velocity of the source;

f₀ is the emitted frequency of source;

Substituting and calculating,

f = $\frac{340}{340+30}$ · 300

f = 275.675 Hz

Thus, the frequency heard by the police officer is 275.675Hz.