A guard on duty observes a fall of 25% in the pitch of the silencer of a motor bike as it crosses him. What will be the speed of car if velocity of sound is 340 m/s ?

A guard on duty observes a fall of 25% in the pitch of the silencer of

1.	A guard on duty observes a fall of 25% in the pitch of the silencer of a motor bike as it crosses him. What will be the speed of car if velocity of sound is 340 m/s ?
Answer» Solution :Before crossing, the source of sound is MOVING towards the listener (guard) `(V_(L) = 0)` `therefore""v' = (V)/(V - V_(s)) v""...(i)` After crossing, the source of sound is moving away from the listener. `therefore""v'' = (V)/(V + V_(s))v""...(II)` As `(v'')/(v) = (75)/(100)` Dividing (i) by (ii) `(v'')/(v) = (V)/(V + V_(s)) v xx (V - V_(s))/(Vv)` `(75)/(100) = (V - V_(s))/(V + V_(s))` `(75)/(100) = (340 - V_(s))/(340 + V_(s))` `75 (340 + V_(s)) = 100 (340 - V_(s))` `75 xx 340 + 75 V_(s) = 100 xx 340 - 100 V_(s)` `75 xx 340 + 175 V_(s) = 100 xx 340` `{:(175 V_(s) = 100 xx 340 - 75 xx 340),(""ul(100 xx 340 - 75 xx 340)),(""175):}` `= (34000 - 25500)/(175) - 48.57` m/s