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 . Calculate the wavelength of the sound wave after it is reflected from the cliff.

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 apparent frequency of the sound reaching the cliff is given by the Doppler effect for a moving source and stationary observer: f' = f₀ ( v v - v_c ) The cliff acts as a stationary source reflecting the sound at this frequency f' . The wavelength of the reflected sound wave is: ' = v f' = v - v_c f₀ Substituting the given values: ' = 335 - 15 400 ' = 320 400 = 0.8 m ' = 80 cm