Redshift? There is no frequency to observe. The light is emitted and when it hits you the timer is stopped. There is no frequency for redshift or blueshift to be observed. The light travels a distance to reach you and when it does the timer stops. Game over.
There is no light without frequency, and there is no frequency stability with relative velocity. Game on.
Again, you are speaking of changing frequency when you are speaking of pitch changing. There is no frequency!!! The sound travels a distance to reach you, PERIOD!
Delete PERIOD, insert COMMA: however, you can hear the pitch change when the firetruck passes, whereas the firemen hear a continuous frequency, and this is the problem that begs to be solved. How does the discrepancy arise between the two observers? Note, if the truck creeps by slowly, you hear no pitch change, therefore distance is irrelevant to your perception of pitch.
We are not throwing many baseballs at a specific interval, we are throwing ONE BASEBALL, and measuring the time of flight until it hits you and the timer is stopped!
This analogy will work for pulsed radar, in which I measure range to target by counting the delay from sending a pulse until the return of the echo, dividing that into 2c to get distance. However, it tells me nothing about speed of the approaching aircraft. In this case (referencing the earliest, "continuous wave" [CW ] radars) I can simply emit a continuous frequency, and scan for the return signal. When I find it offset by a frequency Δf I can calculate the relative velocity Δv. It's relative velocity, so it's how fast he is closing on me or moving away. Δv<0 means he's pulling away. Δv=0 means his range is holding steady. And Δv>0 means he is closing. And these correspond to detected frequency shifts at Δf<0, Δf=0, and Δf>0, respectively.
Until you concede that relative velocity forms the basis for observing frequency shift, you will never be able to explain why the siren wails or how the doppler effect works. Beyond that, you only need to accept that the wave moves at a constant speed regardless of the velocity of the emitter, and you're on your way to batting on an actual sand lot.
I say again, you don't know the difference between frequency and distance!
I say again, you don't know the difference between range and speed!