A car is moving towards an approaching bike. Bike is moving with velocity 30 m/s. Frequency of horn sounded by car is 100 Hz while it is observed by bike rider as 120 Hz. The actual duration of horn is 6 sec. The time the bike rider hears it, in seconds is (take velocity of sound in air as 330 m/s)

Velocity of bike Vb=30m/sLet velocity of car be VCfobs=factual ×Vso+VbVso−Vc 120Hz=100Hz×330+50330−Vc ⇒VC=30m/sDistance between initial and final pulse of horn =Vso ×Δt−VcΔt   {Δt is duration of emission of sound} =(330−30)×6=1800mThis wave train travels with 330 m/s and cross bike rider moving with velocity of 30 m/s towards it.  time taken = length of wave train Vso+Vb =1800330+30=18036=5sec