Do planes have to be noisy? I tend to think of noise as an undesirable waste of energy because the generator was not designed for that purpose. But that doesnt mean this waste can be avoided.
So I wonder how much of this noise is due to flawed design and how much of it is just impossible to get rid of without reducing the plane performance (speed) altogether.
That is, 1. is it possible to make an object fly at low altitude, say 1 kilometer, and still at high speed (say 700 kph), without producing any sound hearable at ground level, and 2. Would that necessarily entail sound reduction techniques that augment energy expenditure?
This is a theoretical question that doesnt require the technology to preexist but still should not violate any known law of nature.
Definitions: the flying object, whatever its shape and method of propulsion should still be able to carry passengers, so e.g. it cannot be flat like a pancake.
 A: Answering your question precisely, while theoretically it is possible, most likely it is very far from being practically possible. 


*

*To fly without (much) noise you need to ensure laminar flow of air around your airplane AND around exhaust of the engines. 

*While laminar flow around the body is currently somewhat achieved for 700km/h and ~10km altitude, it will definitely not be laminar at 1km altitude due to much higher air pressure. You most likely be required ether to reduce speed significantly at 1km or make body much more "slim" (which will increase weight and probably drag).

*Laminar flow from engine exhaust is a much more significant challenge. You will have to make your engines much much larger in cross-sectional area, comparable or exceeding the aircraft body cross-section - which will dramatically increase it's weight. This will allow you to make engine exhaust to be much slower and smoother. Currently it does not look like laminar exhaust from engine at this speed is even remotely feasible. 

*Features like shark-teeth shape of engine exhaust (like General Electric GEnx) does help a little bit, but it is insignificant at the scale that you ask. 

*Active noise canceling is theoretically possible, but would require energy comparable to total engine power (maybe around 10%). Actuators for active noise cancelling with this amplitude currently do not exist. 


You can see that Jet engine designers go with approach #3 : each new generation of Jet engines is getting larger and larger for the same thrust. #4 is cheap improvement. 
A: This topic belongs among the most studied in a branch of acoustics called aeroacoustics and the question is very complex. There is plenty of literature, but if you are ok with some maths, this source provides a good start.
First, let me address your notion about the energy losses due to the emitted noise. Typically the sound has a very low energy compared to the aircraft engines machinery so the emitted power itself is not a great issue. On the other hand, the reasons for the sound radiation might be a problem to be at least optimized if not solved.
There are many formulations for the aeroacoustic wave equations and the trouble is that (although correct) they are not very intuitive. I think the most illustrative is the low Mach number formulation for the stagnation enthalpy $B$
$$
\square B = \nabla \cdot(\boldsymbol{\omega} \ \times \ \mathbf{u} )
$$
where $\mathbf{u}$ is the flow velocity and  $\boldsymbol{\omega} = \nabla \ \times \mathbf{u}$. Therefore you would need to reduce the vorticity $\boldsymbol{\omega}$ and/or fly with vanishingly small speeds which is generally not a good idea. Well, in a rough sketch this is the issue that must be solved, usually at a cost of some trade-offs.
To conclude 


*

*It is not possible to construct an aircraft that strictly does not produce sound (even if it would be a glider)

*Usually, you trade the speed, the noise, the lift and the fuel efficiency. The engineers may just accomplish to get "better bargains" (and they do).

