An engine moving with a velocity of 36 km `//` hour blows a whistle which is heard by a motorist driving with `18km//hr` to be 500 c.p.s. Calculate the actual frequency, when
(a) Two are moving in opposite directions and approaching each other.
(b) Two are moving in opposite directions and receding away.
(c) Two are moving in the same direction , but motorist is behind the engine.
(d) Two are moving in same direction but motorist is in front of engine.
Velocity of sound `=330 ` metre `//` sec

Explanation

Here, `upsilon_(s)=36km//h=100m//s,`
`upsilon_(L)=18km//h=5m//s,`
`v^(')=500cps,v=?`
(a) From figure,
`v^(')=((upsilon+upsilon_(L))v)/(upsilon-upsilon_(s))`
`500=((330+5)v)/(330-10)`
`v=(500xx320)/(335)=477.6c//s`
(b) From figure.,
`v^(')=((upsilon-upsilon_(L))v)/(upsilon+upsilon_(s))`
`500=((330-5)v)/(330+10)`
`v=(500xx340)/(325)=523c//s`
(c) From figure,.
`v^(')=((upsilon+upsilon_(L))v)/(upsilon+upsilon_(s))`
`500=((330+5)v)/(33+10)`
`v=(500xx340)/(335)=507.49c//s`
(d) Figure ,.
`v^(')=((upsilon-upsilon_(L))v)/(upsilon-upsilon_(s))`
`500=((330-5)v)/(330-10)`
` v=(500xx320)/(325)=492.4c//s`