A car is moving towards an approaching bike. the bike is moving with a velocity 30 m s -1 . Frequency of horn sounded by the car is 100 H z , while it is observed by bike rider as 120 H z . The actual duration of horn is 6 s . Find the time interval for which the bike rider hears it. (Take velocity of sound in air as 330 m s -1 )

Step-by-step solution

Velocity of bike V b = 30 m s -1 Let the velocity of car be V c f o b s = f a c t u a l × V s o + V b V s o - V c 120 Hz = 100 Hz × 330 + 30 330 − V c ⇒ V c = 30 m s -1 Distance between initial and final pulse of horn = V s o × Δ t - V c Δ t ( Δ t is duration of emission of sound) = ( 330 − 30 ) × 6 = 1800 m This wave train travels with 330 m s -1 and cross bike rider moving with velocity of 30 m s -1 towards it. Time taken = length of wave train V s o + V b = 1800 330 + 30 = 180 36 = 5 s