A source of sound of frequency `1000 H_(Z)` moves unifornly along a straight line with velocity `0.8` times velocity of sound . An observer is located at a distance `l= 250 m` from this line. Find
(a) the frequency of the sound at instant when the source is closest to the observer.
(b) the distance of the source when he observer no change in the frequency.

Explanation

(a) suppose the pulse which is emitted when the source is at `S` reaches the observer `O` in the same time in which the source reaches from `S` to `S'` , then

`cos theta= (SS')/(SO) = (upsilon_(s)t)/(upsilon t) = (upsilon_(s))/(upsilon) = 0.8`
Now, `f=((upsilon)/(upsilon - upsilon_(s) cos theta)) f`
= `{(upsilon)/(upsilon-(0.8upsilon)(0.8))}(1000)`
`((1)/(1- 0.64)) (1000)`
= `2777.7 H_(Z)`
(b) The observer will observer no change in the frequency when the source is at `S` as shown in figure . In the time when the wave the pulse reaches from `S` to `O` , the source will reach from `S` to `s'` . Hence,

`t= (SO)/(upsilon)= (SS')/(upsilon_(s))`
`:. SS' = ((upsilon_(s))/(upsilon)) SO`
`(0.8) (250) = 200 m`
Therefore, distance of observer from source at this instant is
`S' O = sqrt((SO)^(2)+ (SS')^(2))`
`sqrt((250)^(2)+ (200)^(2))`
`~~ 320 m`