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

The situation is shown in fig.
`SD=sqrt(1^2+0.6^2)=1.166mi`
`costheta=(SC)/(SD)=(1)/(1.166)=0.857`
Thus speed of source along the line of sight is
`v_S=vcostheta=(80)/(60xx60)xx0.857=0.019(mi)/(s)`
Thus the apparent frequency observed is
`n=n_0[(v_(sound))/(v_(sound))]=400[(0.2)/(0.2-0.019)]=442Hz`