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If the source is moved towards the medium at 300m/s, detection can happen when the source is very far away (so very low intensity at the detector) or only for a very short time. Moreover, the solid angle covered by the medium and detector changes as the source moves closer, so interpreting the measurement results would take some care as well.
Perhaps this problem can be overcome by using an oscillator, so that the source movement is sinusoidal. This would allow for longer measurement times and relatively stable relative positions, while measurements would probably still be easily interpreted.
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