A source and an observer are approaching one another with the relative velocity `40 ms^(-1)`. If the true source frequency is 1200 Hz, deduce the observed frequency under the following conditions:
(i) All velocity is in the source alone.
(ii) All velocity is in the observer alone.
The source moves in air at `100 ms^(-1)` towards the observer, but the observer also moves with the velocity `v_(0)` in the same direction.

Explanation

Here V=1200Hz, `v=340ms^(-1)`
Relative velocity `=40ms^(-1)`
(i) Here source move towards the stationary
observer, `v_(s)=+40ms^(-1),v_(0)=0`

`"Train"overset(S" "+ve" "v_(s))tooverset(*)"Observer "v_(0)=0`
`v'=((v-v_(0)))/((v-v_(0)))xxv=(340-0)/(340-40)xx1200`
`=(340xx1200)/(300)=1360Hz`.
(ii) Here observer moves towards the stationary source,
`v_(0)=-40ms^(-1),v_(s)=0`
`S*v_(s)=0" "overset(-ve" "v_(0)" "O)to`
`v'=(v-v_(0))/(v-v_(s))xxv=(340+40)/(340-0)xx1200`
`=(380)/(340)xx1200=1341Hz`.

(iii) Here observer and source move in the same direction,
`v_(s)=100ms^(-1),v_(0)=100-40=60ms^(-1)`
`overset(S" "+ve" "v_(s))to" "overset(S" "+ve" "v_(s))to`
`v'=(v-v_(0))/(v-v_(s))xxv=(340-60)/(340-100)xx1200`
`=(280)/(240)xx1200=1400Hz`.