A car sounding a horn of frequency 1200 Hz passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is 7: 5 . If the speed of sound is ' V ', the speed of the car is

Step-by-step solution

Doppler effect analysis for moving source and stationary observer: Given horn frequency f = 1200 Hz and speed of sound V , let v_s be the car's velocity. The observed frequency ratio is f_ before f_ after = 7 5 . Using Doppler formulas: f_ before = f ( V V - v_s ) when approaching, f_ after = f ( V V + v_s ) when receding. Substitute into ratio: f ( V V - v_s ) f ( V V + v_s ) = 7 5 Cancel f and V : V + v_s V - v_s = 7 5 Cross-multiplying: 5(V + v_s) = 7(V - v_s) Simplify: 5V + 5v_s = 7V - 7v_s 12v_s = 2V v_s = V 6