I actually worked in the same building as the people organizing this research. Now I'm drawing on decade-old memory, and the program may have changed in the interim, but at that time the research that would become the X-59 demonstrator was absolutely about eliminating the sonic boom. There is no law of nature that says you have to have a sonic boom when you break the sound barrier--there are in fact a lot of assumptions wrapped up in that outcome.
A sonic boom is what you get when a traditional solid, largely flat-ish airfoil pushes air smoothly through the transition to supersonic flight. Very ELI5, but during the transition the energy/noise being put into the air basically stops dissipating from the aircraft at the point of transition, and so all that noise clumps together into a shockwave.
The shape of the X-59 makes it such that the transition doesn't happen uniformly over the air surfaces of the plane at the same time. It does get a little noisier around the transition, but it not a shockwave at all.
If that's so then apologies, my bad - I didn't see any details in this NASA news so just assumed it was similar logic to Boom Aerospace, whose strategy I believe is to somehow make the boom noise aim away from the ground (partly directly, and partly by figuring out a way to make sure that sound waves heading downwards bounce off the atmosphere back upwards, so that the boom exists just not audible to people at ground level).
And TIL I learn that it's even possible to break the sound barrier without a boom of some kind (assuming NASA haven't found otherwise and adopted Boom's strategy in the years since you were hearing about it from them). Cheers for the interesting comment!
Edit: although I hope somebody can answer sroussey's original comment of «What happens when there are 1000 flights over land all having sonic booms, and 1000 reflecting sonic booms, and the 1001 plane flies through all the sonic booms?», since if Boom are successful I assume they're more likely to have thousands (or at least enough to have overlapping flights at times) of planes in the air than NASA. Unless, I guess, NASA do such a good job of demonstrating that you can actually get rid of the boom rather than just redirecting where the sound waves go that Boom change their strategy to that and/or get outcompeted by rival companies doing the NASA way. ("Just" is a little unfair, since Boom's technique seems incredibly clever to me.)
All good. I know less about Boom's technology, but yeah from what I understand they took a different approach: redirect the sonic boom up and out so that it it spends more time traveling through the atmosphere and isn't so loud once it hits the ground. The X-59 solution is to not make a sonic boom in the first place. You can't eliminate the noise entirely, but with the X-59 they talk about a "sonic thump" that is qualitatively of a different order.
It's a bit like stealth tech: early "low observable" fighter planes did things like switch to unibody cockpits so there were fewer reflective interfaces and therefore a smaller radar cross section. Then the F-117 and B-2 went with "be fucking invisible to radar" (or approximately so). Totally changes the game.
A "sonic thump" will be noisier than normal operating engine noise. You will hear it and it will be noticeable in the sense that unlike regular airplane takeoff and landing, it will be a distinct transitory sound.
But in terms of absolute noise levels and mechanical properties, the "sonic thump" of a commercial airline would probably be considerably quieter than, for example, the regular takeoff/landing noise of a military jet. It needs to be characterized and understood to see what the effect would be on communities living near supersonic airports, but not a real engineering concern.
Your question is valid with respect to Boom though, and that is part of their challenge to getting regulatory approval for supersonic transition over land.
A sonic boom is what you get when a traditional solid, largely flat-ish airfoil pushes air smoothly through the transition to supersonic flight. Very ELI5, but during the transition the energy/noise being put into the air basically stops dissipating from the aircraft at the point of transition, and so all that noise clumps together into a shockwave.
The shape of the X-59 makes it such that the transition doesn't happen uniformly over the air surfaces of the plane at the same time. It does get a little noisier around the transition, but it not a shockwave at all.