Travelling towards a cliff, a car moves with a speed of 54 km h ⁻¹ . The car's horn emits sound at a frequency of 400 Hz , and the speed of sound is 335 m s ⁻¹ . What frequency does a person sitting inside the car hear for the reflected sound wave?

Step-by-step solution

Speed of the car, v_c = 54 km h ⁻¹ = 54 5 18 m s ⁻¹ = 15 m s ⁻¹ Frequency of the horn, f₀ = 400 Hz Speed of sound, v = 335 m s ⁻¹ The sound is reflected from the cliff. The cliff acts as a stationary observer for the incident sound and as a stationary source for the reflected sound. The apparent frequency heard by the person in the car is given by the Doppler effect formula for a source and observer approaching each other: f' = f₀ ( v + v_c v - v_c ) Substituting the given values: f' = 400 ( 335 + 15 335 - 15 ) f'