Question

Why doesn't proximity have anything to do with the Doppler Effect?

Answer 1

The Doppler effect assumes that sound travels through the same medium throughout. Now sound travels at a specific speed dependent on the temperature of the medium.
\[\huge f' = f ({ {v +v_0} \over {v-v_s}})\]
Sound doesn't travel in one direction, it just is easier to visualize then drawn that way. If that makes sense.