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 . What frequency will a person standing near the track hear whom the train has just passed?

Step-by-step solution

Speed of the train, v_s = 108 km h ⁻¹ = 108 5 18 m/s = 30 m/s Speed of sound, v = 340 m/s Actual frequency, f₀ = 500 Hz Since the train has just passed the person, it is moving away from the stationary observer. Using the Doppler effect formula for a source moving away from a stationary observer: f = f₀ ( v v + v_s ) Substituting the values: f = 500 ( 340 340 + 30 ) f = 500 ( 340 370 ) f = 17000 37 459.46 Hz The frequency heard by the person is approximately 459 Hz .