If source does not move along the line SO. what will be the apperent frequency at O

Explanation

The changed frequency `f'` is now,
`f' = f ((upsilon)/(upsilon - upsilon_(s) cos theta))`
This time `f'` is not constant but it is a function of `theta` , which is variable. But , at a far distance,
`theta rarr 0^(@)` or `cos theta rarr 1` or
`:. f'= f ((upsilon)/ (upsilon - upsilon _(s)))`
and this is the maximum value of `f'` (say `f_(max)`)
At point `P, theta = 90^(@)`
`:. f' = f`
During receding (to the right of `p`)
`f' = f ((upsilon)/ (upsilon - upsilon _(s)costheta))`
again, at large distance from `P`,
`theta rarr^(@)` or `cos theta rarr 1`
`f' = f ((upsilon)/ (upsilon + upsilon_(s)))`
This time, this is the minimum value of `f'` (say `f_(min)`).
Hence, `f'` varies from `f _(max)` to `f _(min')` with `f' = f` at the time of crossing `p` .
The correct `f'` versus `t` graph is as shows below.