Can a sonic boom be a standing wave? If I understand the sonic boom of a supersonic aircraft correctly, it can be abstracted as an (ideally) conical wavefront dragging behind the vehicle, with the “boom” being the perception of the edge of that cone passing the observer.
A standing wave, by definition, doesn’t move in space but merely oscillates in time. So from the perspective of someone stationary on the ground, the sonic boom obviously can’t be a standing wave.
But from the perspective of the aircraft itself, or anything along the wavefront keeping pace, wouldn’t that make a sonic boom at Mach 1 a standing wave? What about at speeds greater than Mach 1, or at hypersonic speeds? What about when the aircraft is accelerating (forward or back) vs. cruising at constant speed?
 A: In its simplest form, a shock wave is a stationary wave.  This means there is a reference frame where the shock would appear to be a standing wave.

But from the perspective of the aircraft itself, or anything along the wavefront keeping pace, wouldn’t that make a sonic boom at Mach 1 a standing wave?

Yes.

What about at speeds greater than Mach 1, or at hypersonic speeds?

This just changes the angle of the Mach cone, $\alpha$, given by:
$$
\sin{\alpha} = \frac{ C_{s} }{ V }
$$
where $C_{s}$ is the speed of sound and $V$ is the speed of the piston/driver of the shock.

What about when the aircraft is accelerating (forward or back) vs. cruising at constant speed?

If the piston/driver is accelerating, then the system is no longer stationary as there is no reference frame where the shock would be at rest.

A standing wave, by definition, doesn’t move in space but merely oscillates in time.

Just a side note, this isn't formally correct.  Well, perhaps misleading is a better word.  I say this because this would depend upon reference frame.  There will be a reference frame where a standing wave appears to move and one where it appears to not move in space.  The more correct phrasing would be that a standing wave is a stationary wave, i.e., there exists a reference frame where the wave appears at rest.
