What is the basic cause of a sonic boom.

To help understand how a sonic boom is created we must
first understand the nature of a sound wave created in air by a stationary object and
what happens when waves interfere with each other.

Sound is
created when a vibrating object disturbs a medium, causing the molecules in the medium
to alternately compress and rarefact (separate) in rhythm with the object's vibrations.
 In the case of sound we normally hear, the medium is air (although it does not have to
be which is why we can hear sounds underwater).  If the object is allowed to vibrate
freely in open air on a calm day, the compressed and rarefacted molecules of air will
transfer the vibrations to molecules close to them.  Those molecules will transfer the
vibration to molecules next to them, etc...  The result is a "wave" of compressed air
moving away from the source of the vibration in all three directions simultaneously.
 These waves of sound have a speed called the "speed of sound" which is determined by
the atmospheric conditions in the area where the sound is
created.

The intensity, or "loudness", of the sound gets
less the further away the compression moves from the source.  In fact it obeys the
"inverse square law" which means that for each time it doubles the distance from the
source, the sound becomes 1/4 as intense.

When two waves
overlap, they interfere with each other.  For the purposes of a sonic boom we need only
concern ourselves with constructive interference.  In constructive interference the
pressure and rarefaction of the the two waves overlap.  When this happens the pressures
add together making an even stronger wave.  If three waves overlap and constructively
interfere there is an even stronger pressure wave created producing a more intense
(louder) sound.  The more waves that constructively interfere with each other, the more
intense the resulting pressure becomes.

In the case of a
plane creating a sonic boom, the plane moving through the air makes a pressure wave by
pushing air out of its way as it moves forward.  It is not vibrating as in the simple
example above, but it is making pressure in the air which we can hear as sound.  The
sound leave the plane in all directions, but is most intense in front of the plane.  As
the plane approaches the speed of sound, the new wave it creates overlaps the wave it
created earlier causing constructive interference.  When the plane reaches the speed of
sound, all of the sound it is creating and pushing out in front of the plane is
overlapping all of the sound it has just created producing a lot of constructive
interference.  The result is one huge wave of pressure that builds up in front of the
plane.  Even though the plane may be far away, and the sound has to obey the inverse
square law, there is so much pressure created by the plane moving at the speed of sound
that the intensity of the sound is still very high when it reaches the ground. When that
pressure reaches our ears we hear it as a loud explosion of sound.  It is that loud
"boom" of a single, large wave of pressure hitting out ears that we call a sonic
boom.