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 figure-6.90.

`SD = sqrt(1^(2) + 0.6^(2)) = 1.66` miles
`cos theta = (SC)/(SD) = (1)/(1.166) = 0.857`
Thus speed of source along the line of sight
`v_(s) = v cos theta = (80)/(60xx60) xx0.857`
= 0.019 miles/s
Thus the apparent frequency observed is
`n = n_(0) [v_(sound)/(v_(sound) -v_(s))] = 400[(0.2)/(0.2 - 0.019)]` = 442 Hz.