A car travelling at 108 km h ⁻¹ encounters another car ahead of it moving in the same direction at 72 km h ⁻¹ . The first car sounds a horn with a dominant frequency of 800 Hz . Determine the apparent frequency heard by the driver in the front car. The speed of sound in air is 330 m s ⁻¹ .

Step-by-step solution

Speed of the first car (source), v_s = 108 km h ⁻¹ = 108 5 18 m s ⁻¹ = 30 m s ⁻¹ Speed of the second car (observer), v_o = 72 km h ⁻¹ = 72 5 18 m s ⁻¹ = 20 m s ⁻¹ Actual frequency of the horn, f = 800 Hz Speed of sound, v = 330 m s ⁻¹ The source is moving towards the observer and the observer is moving away from the source. Using the Doppler effect formula for apparent frequency: f' = f ( v - v_o v - v_s ) Substituting the given values: f' = 800 ( 330 - 20 330 - 30 ) f' = 800 ( 310 300 ) f' = 800 31 30 f' = 2480 3