Is there a Doppler shift if both the source of sound and the receiver of the sound are moving at the same velocity and in the same direction relative to the air? Give a physical explanation. (It is not enough to just state and apply formulas.)

Solution
NO. Seen from the point of view of the medium the movement of the source
compresses (or expands) the wavelength, but the motion of the listener has
an exactly compensating effect of expanding (or compressing) the wavelength.
This is really due to the fact that the distance between the source and the
listener is not changing and so just a many wavefronts as are emitted per
second will be received. (This answer changes if both source and listener
are moving faster than the speed of sound in the medium.)

Physics 102 HW page