A violin player travelling on a slow train sounds a 440 Hz note, while another violin player standing beside the track produces the identical note. As the train approaches the person on the ground when they are near each other, the person on the ground detects 4.0 beats per second. Given the speed of sound in air is 340 m/s , what beat frequency is detected by the player on the train?

Step-by-step solution

Let f = 440 Hz be the actual frequency of the note. Let v be the speed of sound and v_s be the speed of the train. For the observer on the ground, the source (train) is moving towards them. The apparent frequency heard by the person on the ground is: f₁ = f ( v v - v_s ) The beat frequency detected by the ground observer is: f₁ = f₁ - f = f ( v v - v_s - 1 ) = f ( v_s v - v_s ) = 4.0 Hz For the observer on the train, the source on the ground is stationary and the observer is moving towards it. The apparent frequenc