A locomotive approaching a crossing at a speed of 80 mi/h sounds a whistle of frequency 400 Hz when 1 mi from the crossing. There is no wind, and the speed of sound in air is 0.200mi/s. What frequency is heard by an observer 0.60 mi from the crossing on the straight road which crosses the railroad at right angles?

Explanation

As is clear from figure
`SC=1"mile"`
`CL=0.6"mile"`
`SL=sqrt(SC^(2)+CL^(2))=sqrt(1^(2)+0.6^(2))`
`=sqrt(1.36)=1.166mil e`
`costheta= (SC)/(SL)=(1)/(1.166)=0.857`
`v=0.2mil e//sec.`
`v=400Hz,v_(s)=80mil es//hour`
`=(80)/(60xx60)mil e s//sec`
Velocity of source (engine) along SL
`v_(s)=v_(s)costheta=(80xx0.857)/(60xx60)=0.019mil e//sec`
As `v_(')=(upsilonxxv)/(upsilon-upsilon_(s)^(')) :. v^(')=(0.2xx400)/(0.2xx0.019)=442Hz`