A

Step 1: Understand the Doppler's Effect. The Doppler effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the wave source.
Step 2: Identify the conditions in which the Doppler effect applies. The effect is most notable when there is relative motion between the source and the observer of the sound.
Step 3: Analyze each option:
- Option A: If the sound source velocity is equal to the velocity of sound, the waves cannot propagate ahead of the source, because the source is moving away at the same speed that the sound is travelling. This results in a scenario where the Doppler effect does not manifest because all waves are generated but do not advance.
- Option B: If the sound source velocity is less than the velocity of sound, the observer will experience a higher frequency than the source emits when the source approaches and a lower frequency when it recedes, demonstrating the Doppler effect.
- Option C: If the sound source velocity is greater than the velocity of sound, it creates shock waves, resulting in a sonic boom, which is another manifestation of the Doppler effect.
- Option D: If the velocity of the sound source is zero, there is still a stationary source emitting sound, and the observed frequency will remain constant as there is no relative motion.
Conclusion: Therefore, the Doppler effect does not apply when the source's velocity is equal to the velocity of sound (Option A).