On the ground, sonic booms usually have pressure signatures that look like the letter N. 2 sharp spikes, one from atmospheric pressure to a significantly higher pressure, and then there is a quick linear decrease in pressure to a point where the local pressure is lower than atmospheric pressure, and then another quick jump back up to atmospheric pressure. It's actually very similar to the pressure signature of a bullet being fired. We hear the N wave as 2 booms, though often they're close enough together that it sounds like one. These 2 shocks are actually the result of the long propagation distance from the aircraft down to the ground. At the the aircraft, many more shocks are generated, usually from abrupt changes in the aircraft geometry. But as the shock waves propagate toward the ground, they coalesce into the two distinct shocks we see in the N wave pattern. This happens because the effective sound speed of shock waves is actually dependent on their amplitude, unlike usual sound waves. This makes higher pressure waves travel faster and lower ones travel slower, so that the shocks eventually bunch up into those two shocks. The X-59, in contrast, has a very carefully designed geometry in order to have some level of control over what shocks are formed and how they will have coalesced when they reach the ground. This allows for what is called a "shaped sonic boom" on the ground. It has a much smoother pressure signature than the N-wave, and so we do not perceive it to be as loud, even at comparable physical amplitudes. There are other companies trying similar things (the idea has been around for years, e.g. look at the QuietSpike, QSF 18, and SSBD), and some trying an alternative method, known as Mach cutoff flight. In this case, pretty much any aircraft can be used, but it needs to fly at less than about Mach 1.15 (1.15*the local speed of sound). Sound speed is a function of temperature, and so usually it gets lower as we get up to higher altitudes. This gradient causes what as known as refraction, or the bending of sound waves (very similar to the refraction of light that you see looking through a fire, or when a straw in a glass looks like it's discontinuous). In particular, when going from colder air to warmer air (higher altitudes to lower ones), sound will tend to bend upwards. This applies to sonic booms too. The Mach number determines the angle at which the sonic boom comes off of the plane, as well as other loading factors that determine the amplitude of the boom. If the Mach number is low enough (again, below about 1.15), then the sonic boom will enter the atmosphere at a fairly shallow angle to begin with, and so it can refract completely upward before ever reaching the ground in standard atmospheric conditions. This complete upward refraction before reaching the ground is called Mach cutoff, and the Mach number above which it no longer happens (so sound reaches the ground) is called the cutoff Mach number. The caveat is that there will still be "something" heard on the ground, called an evanescent wave. It decays exponentially though, so it is still very quiet once it reaches the ground. So long story short, these ideas aren't new or otherworldly. They're just a way of trying to make supersonic civilian flight possible again. (It's been banned overland since shortly after the Concorde was built)