A person standing on a road transmits a sound signal to the driver of a car moving away from him at 72 km h ⁻¹ . The signal, travelling in air at 330 m s ⁻¹ with a frequency of 1600 Hz , reflects off the body of the car and returns. Determine the frequency of the reflected signal heard by the person.

Step-by-step solution

Speed of the car, v_c = 72 km h ⁻¹ = 72 5 18 m s ⁻¹ = 20 m s ⁻¹ Speed of sound, v = 330 m s ⁻¹ Original frequency, f₀ = 1600 Hz The frequency received by the car (acting as an observer moving away from the stationary source) is given by: f₁ = f₀ ( v - v_c v ) The car then reflects the sound, acting as a moving source moving away from the stationary person. The frequency heard by the person is: f₂ = f₁ ( v v + v_c ) Substituting f₁ into the equation for f₂ : f₂ = f₀ ( v - v_c v ) ( v v + v_c ) = f₀ ( v - v_c v + v_c