In the jetliner biz we are getting aircraft engines quiet enough now that most of the noise on approach is just the plane passing through the air. The manufacturers are working hard to further reduce that by careful testing of flap designs & landing gear shapes to minimize turbulence.
Nevertheless, there is a lower theoretical limit to how much noise even an unpowered plane can make as it continuously disturbs the air to hold itself up. And there is a much higher practical limit as well.
On takeoff & climbout you have the additional challenge of providing the power to accelerate the aircraft & to force it to climb. The only way you can apply that power usefully using today’s technology is to move air aft, thrusting the plane forwards. Until / unless we develop anti-gravity, that action / reaction is the only vailable technique.
Any mechanism we use to force air aft introduces turbulence, aka noise. Certainly reduced noise can be designed for: a 1980s 757 produces barely 0.1% of the noise of a 1960s 707, while otherwise being almost identical in size, weight & speed.
For typical aircraft which spend most of their time at high altitude, distance to the ground provides a great natural muffler at little or no cost. In fact the 757, just by climbing much better than it’s predecessor 707, produces a much smaller noise impact footprint even before you consider the reduced engine noise at the source.
There are in fact mandated noise standards which are getting tougher every few years. Aircraft are expensive capital assets with 30+ year economic lives, so the standards can’t move too fast without greatly disrupting the industry economics. Check out 14CFR36 for more details.
