Two trains are moving towards each other, each with a speed of 90 km h ⁻¹ . If one train sounds a whistle at 500 Hz , determine the apparent frequency heard in the other train. The speed of sound in air is 350 m s ⁻¹ .

Step-by-step solution

Speed of each train, v_s = v_o = 90 km h ⁻¹ = 90 5 18 m s ⁻¹ = 25 m s ⁻¹ Speed of sound, v = 350 m s ⁻¹ Actual frequency, f = 500 Hz Using the formula for Doppler effect when both source and observer are moving towards each other: f' = f ( v + v_o v - v_s ) Substituting the given values: f' = 500 ( 350 + 25 350 - 25 ) f' = 500 ( 375 325 ) f' = 500 ( 15 13 ) f' = 7500 13 576.92 Hz Rounding off to the nearest integer, the apparent frequency is 577 Hz .