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)

Question

Infinity Learn · Accepted Answer

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 $$Vso+Vb$$ $$=1800330+30=18036=5sec$$

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)

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