Non-throbbing, silent-compressor window air conditioner?
The source of the noise is the motor, compressor and fans spinning.  A DC air conditioner would make the same sounds. 

The AC power frequency enters the picture because the cheapest-to-build motors are induction motors, which spin at slightly less than line frequency.  As such the noise frequencies tend to be in the 48-49 Hz or 58-59 Hz range. 

Often there is also a "rattle" from something coming loose. A healthy unit should not rattle, but this is rather hard to fix. 

The reason air conditioners are flippin' loud is they are cheap.  Of course there is consumer demand for quieter air conditioners, and the units are out there for the discerning shopper.  They are more money and most people don't want to pay it.  Or when they are shopping it doesn't occur to them to make it a priority.