What do we hear, on the ground, from a helicopter in flight?
Rotor noise is relatively complicated, and is very highly dependent on the design of that particular aircraft. Here are at least a few components to consider:

Ultimately what you're "hearing" is of course pressure waves in the air, which in a helicopter are almost entirely caused by the rotors passing through said air[1].  If you're head-on and a fair distance away, you're primarily hearing the pressure wave that's generated as the rotor passes the point where it directly points at you, because that's where you get the strongest component of pressure "pointed" in your direction.

As the aircraft moves, your orientation to the sound profile changes: you get both the doppler effect which changes the pitch, but you also get a very different sound profile because the pressure waves from the main rotor are interacting with both the body of the aircraft and more importantly the pressure waves from the tail rotor in different ways.  I don't remember the exact percentage, but a very large part of the sound generated by helicopters is the interaction of the main and tail rotors - this is a main reason that you see a lot of modern helicopters with a "shrouded" tail rotor. If you're truly head-on, it's reasonable to assume that you're getting very little of the interference with the tail rotor, and as you get more side-on with the aircraft you get far more interference noise.

[1] You also, of course, get noise from the engine-- but that's usually drowned out unless you're quite close, OR if you happen to be sitting near a chopper with the rotor at zero-lift... in this case the noise from the rotor is actually pretty low and you can hear the engines and the tail rotor a lot more clearly...