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 reflected whistle as received by the boy.

Step-by-step solution

Speed of the boy, v_ b = 12 km h ⁻¹ = 12 5 18 m s ⁻¹ = 10 3 m s ⁻¹ The boy acts as a source moving towards the stationary wall. The frequency of the sound reaching the wall is: f₁ = f₀ ( v v - v_ b ) The wall reflects the sound with the same frequency f₁ . Now, the boy acts as an observer moving towards the stationary wall. The frequency of the reflected sound received by the boy is: f₂ = f₁ ( v + v_ b v ) = f₀ ( v + v_ b v - v_ b ) Substituting the given values: f₂ = 1600 ( 330 + 10 3 330 - 10 3 ) f₂ = 1600 ( 990