A train approachign a railway crossing at a speed of `120 kmh^-1` sounds a short whistle at frequency 640 Hz when it is 300 m away from the crossing. The speed of sound in air is `340 ms^-1`. What will be the frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of 400 m from the crossing ?

Explanation

Here, `upsilon_(s)=120km//h=(120xx1000)/(60xx60)m//s`
`=(100)/(3)m//s`
`v=640Hz. upsilon=340m//s, v^(')=?`
In figure ,
`AC=300m`
`CB=400m`
`:. AB=sqrt(AC^(2)+CB^(2))`
`sqrt(300^(2)+400^(2))=500m`
Let `/_CAB=theta`
`:. costheta =(AC)/(AB)=(300)/(500)=(3)/(5)`
Component of velocity of source along AB
`=upsilon_(s)costheta=(100)/(3)xx(3)/(5)=20m//s`
As the source is approaching the listener, with velocity `upsilon_(s)costheta`, therefore apparent frequency,
`v^(')=(upsilonxxv)/(upsilon-upsilon_(s)costheta)`
`v^(')=(340xx640)/(340-20)=680Hz`