Why is it that the sonic boom only occurs at the moment the plane crosses Mach 1?
The answer is: It doesn't. Sonic boom first occurs when the plane crosses Mach 1 and the plane continues producing sonic boom as long as the speed stays above Mach 1.
Another part of your question is:
How come sonic booms only occur once?
And the answer is: because the plane flew over you once. If the plane were to turn around and fly over you a second time you'd hear two sonic booms.
When you hear a sonic boom it doesn't mean that that boom was generated at Mach 1. It only means that the boom was generated at speeds equal to or greater than Mach 1. For example, a plane travelling at Mach 3 would still produce a sonic boom but you'd still only hear it once because the “boom” would only reach your ear once.
To understand this you need to understand what a sonic boom is.
Various parts of the airplane generate sound. Form the roar of the jet engines to the whistle of the skin of the aircraft moving through the air.
When travelling at normal subsonic speed. These sounds travel normally through the air and what you hear is a continuous sound of an airplane flying.
When travelling at or faster than the speed of sound, all these sounds arrive at your ear simultaneously. That is to say, if normally you'd be able to hear a plane passing overhead over a period of 10 seconds (for example) then at supersonic speeds all those 10 seconds of sounds (engine roar, woosh of the wings etc.) arrive at your ear at the same moment.
Since all the sounds you'd ever hear from the airplane arrive at the same time, the result is a very loud boom (all the 10 seconds or more of sound added together).
That's why you only hear it once typically.
There are exceptions though. If the plane is long enough, and the nose and tail generate loud sounds, it is possible to experience a double sonic boom caused by the tail generating a second boom. But generally, even a very long plane like the 747 or A380 (or Concorde) would take only a very tiny fraction of a second to travel the length of their body at supersonic speeds. You'd probably need a plane a mile long to experience a proper double boom.
You’d probably need a plane a mile long to experience a proper double boom.
So, a UFO a mile long traveling at super sonic speed
would do it? Got it.
“...To understand this you need to understand what a sonic boom is.
Various parts of the airplane generate sound...
When travelling at or faster than the speed of sound, all these sounds arrive at your ear simultaneously...all those 10 seconds.. arrive at your ear at the same moment...(all the 10 seconds or more of sound added together).
That’s why you only hear it once typically.
There are exceptions though. If the plane is long enough, and the nose and tail generate loud sounds, it is possible to experience a double sonic boom caused by the tail generating a second boom... You’d probably need a plane a mile long to experience a proper double boom.” [RGSpincich, post 22]
These phrases are wildly in error. The website where you found them might not be trustworthy.
A “sonic boom” is a shock wave. A shock wave is generated in our planet’s atmosphere by any material object traveling in excess of the local speed of sound, a speed referred to in technical jargon as “Mach 1.0”. The speed is never constant but varies with local conditions such as atmospheric pressure, temperature, humidity, particulate content etc. Temperature is by far the largest factor; the colder it gets, the slower the local speed of sound is.
The “boom” heard by observers on the ground is the air pressure changing suddenly as the shock wave travels over them.
Shock waves have nothing to do with sounds generated by the traveling object; bullets traveling faster than Mach 1.0 generate shock waves also.
An aircraft may generate more than one shock wave; they tend to emanate from sharp features like noses, wing edges, vertical & horizontal stabilizers, and the like. This is why more than one boom may be heard in quick succession. Shock waves also reflect off the surface of the earth and large solid objects like buildings, or topographic features like cliffs or canyon walls. In this way, additional booms sometimes make themselves heard. Think of them as echoes.