It’s a combination of factors, one of which is that a prop is just out there, unshielded like the fans inside a jet engine (which still make a ton of noise in the case I’d high bypass models). Then there’s cortex shedding, which is mostly occurring along edges and tips. Airplanes also tend to fly at much higher altitudes except on takeoff and landing, or their noise would be an issue too. Finally you’re right that the number and arrangement of blades matters, because each blade produces some turbulence, vortices, etc which then interact with the next blade in sequence. All told the issue is just s high degree of aerodynamic noise. You get that with a wing and any aerodynamic body, and really if you’ve ever seen model jets fly you’ve heard the racket they make.

The major issue is that until drones came around, you didn’t have to worry very often about large number of high performance aircraft operating throughout civilian airspace, at very low altitudes in crowded areas.

A plain wing is way less noisy, though. Construct a glider with the same mass as a typical quadcopter and you’ll be hard pressed to hear any noise from it, despite the fact that the wing is unshielded and has edges to shed vortexes from.

Oh sure, but the glider is moving through the air at a stately pace (generally between 50-95mph), shedding vortices without anything coming behind them to crash into them. A prop operates at much higher speeds, typically between 450-720mph!

Really? I arbitrarily looked up the DJI Phantom 3 and found a max RPM of about 8000 with a prop diameter of 9 inches, which gives a tip speed of about 200 MPH at the most.

That’s still pretty fast, of course. That points to using bigger props as a potential way to cut noise.

You’re right, I was looking at max motor rpm, whoops!

A lot of things: the high rpm motor powering it, the combined area of the blade edge that is higher than the area of the wing edge, and the higher pressure differential between the air behind the propeller compared to the air in front of it. The sound results from this pressure differential collapsing so anything that increases the pressure differential will create more sound.

Both propellers and wings are fundamentally the same thing: airfoils.

However, air passes over a propeller much, much faster than over a wing, and creates shock waves in a way that wings don't.

Does it? The same airfoil needs the same speed to provide a given amount of lift, regardless of whether it’s a wing or a propellor.

The speed of a propeller is low close to the rotor, and sometimes faster than sound at the extremity of the blades. Can’t reduce sound on that.

Propeller efficiency takes a nose dive when the tips go supersonic. Most props therefore do not operate in this range.

Wings don't rotate and thus don't efficiently produce sound waves.