A train travelling at 108 km h ⁻¹ towards east whistles with a dominant frequency of 500 Hz . The speed of sound in air is 340 m/s . A wind begins blowing towards east at a speed of 36 km h ⁻¹ . Determine the frequencies heard by a passenger in the train and by a person standing near the track whom the train has just passed.

Step-by-step solution

Velocity of the train, v_s = 108 km h ⁻¹ = 108 5 18 = 30 m/s Velocity of the wind, v_w = 36 km h ⁻¹ = 36 5 18 = 10 m/s For the passenger sitting in the train, the relative velocity between the source (train whistle) and the observer (passenger) is zero. Therefore, there is no Doppler shift, and the frequency heard by the passenger is equal to the actual frequency, which is 500 Hz . For the person standing near the track whom the train has just passed, the train is moving away from the person. The sound travels from