Two trucks heading in opposite directions with speeds of 60 kmph and 70 kmph respectively, approach each other. The driver of the first truck sounds his horn of frequency 400Hz. What frequency does the driver of the second truck hear ? (Velocity of sound `= 330 m //s `).After the two trucks have passed each other, what frequency does the driver of the second truck hear ?

Explanation

`v_(s) = 60 kmph = 60 xx ( 5)/( 18) m //s = ( 300)/( 18)m //s `
`v_(0) = 70 kmph= 70 xx ( 5)/( 18) m//s = ( 350 )/( 18) m //s`
`v = 400 Hz`
When two trucks approach each other
`v' = v[ ( v+ v_(0))/(v-v_(s))]`
`T_(1) overset(v_(s))(rarr) overset(v_(0))(larr)T_(2)`
`implies v'= 400[(330+(350)/(18))/(330-(300)/(18))]`
`= 400[ ( 33 xx 18+ 35)/( 33xx 18 - 30)]`
` = 400xx ( 629)/( 564)`
`:. v' = 446 Hz`
When two trucks crossed each other,
`v^(1) = v[ ( v-v_(0))/(v+v_(s))]`
`overset(v_(s))(larr)T_(1)" "T_(2)overset(v_(0))(rarr)`
`implies v' = 400[ ( 330 - ( 350)/(18))/(330 + ( 300)/( 18))] = 400[( 594-35)/( 594+30)]`
`=:. v' = 358.33Hz`