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 . How many beats does a person in the car hear in 10 seconds between the direct sound from the horn and the sound coming after reflection?

Step-by-step solution

Speed of the car, v_c = 54 km h ⁻¹ = 15 m s ⁻¹ . The frequency of the direct sound heard by the person in the car is the same as the original frequency, since there is no relative motion between the person and the horn: f₁ = 400 Hz For the reflected sound, the car acts as a moving source approaching the stationary cliff, and the person in the car acts as a moving observer approaching the stationary cliff. The apparent frequency of the reflected sound heard by the person is: f₂ = f ( v + v_c v - v_c ) Substituting t