While riding a bicycle towards a vertical wall at 12 km h ⁻¹ , a boy whistles at his dog on the ground. Given that the whistle has a frequency of 1600 Hz and the speed of sound in air is 330 m s ⁻¹ , determine the frequency of the whistle as received by the wall.

Step-by-step solution

Speed of the source (boy on the bicycle), v_s = 12 km h ⁻¹ = 12 5 18 m s ⁻¹ = 10 3 m s ⁻¹ Frequency of the source, f = 1600 Hz Speed of sound in air, v = 330 m s ⁻¹ The wall acts as a stationary observer while the source is moving towards it. Using the Doppler effect formula for a moving source and a stationary observer, the apparent frequency f' received by the wall is given by: f' = f ( v v - v_s ) Substituting the given values: f' = 1600 ( 330 330 - 10 3 ) f' = 1600 ( 330 990 - 10 3 ) f' = 1600 ( 990 980 ) f' =