Perhaps we are all discussing the same thing. A single pulse is one complete cycle/Hz of the ultrasonic sound. If the Doppler effect is measurable on 100 cycle sound pulse, it must be the same for each of those 100 cycles.
But that's not the way a single pulse is defined.Are you using cycle and Hz interchangeably? If so then you need the start of a second waveform to define a particular period or frequency. An isolated single pulse just has a duration but not a frequency.
I agree. This singular wave has a pressure peak and trough, and maybe another peak (or trough) if exactly timed. The arrival time of the half-wave can be used to calculate the single-cycle frequency, but not change in freq or phase shift
Re-read the PM I sent you. Doppler only senses objects moving relative to the observer. You have outgoing and incoming waves, it works nicely but your waves have to be clean to get full detail.
I was under the impression that a doppler sensor uses a continuous wave (CW) signal rather than a single pulse.
At least one doppler radar used short pulses to operate, we didn’t sense the whole many Km return with ground observing radar as that would be too much all at once, radar travels 300m/microsec go figure.
With sound, study bats and dolphins.
Blind cyclist uses echolocation to navigate.
Compared to that, you can get 40-42 samples/second with a standard ping module out to 4 meters and get clean returns that don’t pick up echoes.
That's what I was assuming in post #28. The current discussion came up after that and I was trying to understand the theory behind the single pulse method.. unsuccessfully. 
There are apparently several other kinds of Doppler, pulse-pair, multi-lag autocorrelation, FFT, etc.
I imagine the return signal from the ubiquitous hobby US range finder is very low amplitude and buried in noise as well. I think comparing its pulse width with the transmitted single pule in any meaningful way would be difficult.
There was a discussion about the HC-SR04 US rangefinder in an earlier topic that I can't find. One of the forum's regular helpers posted links to a couple of articles that I did have the presence of mind to save in my Reading List.
In these two articles, the authors describe in detail how the module works along with scope traces of the various signals and a schematic of the circuit. From this, OP might get some pointers on how to modify one or two of the modules to do Doppler speed measurement instead of ranging.
Since the receiver circuitry includes bandpass filtering to limit the response to 40 kHz one would have to bypass or modify that so that the delta-f was preserved.
