A shock-wave pattern is formed around an aircraft when ?ying at supersonic speed (i.e. faster than sound). Sonic boom is the noise from these shock waves, as heard at the ground. Sonic booms are weak shocks: the typical over pressure at the ground is up to 100 Pa, a shock strength of order of the atmospheric pressure. The disturbance due to the motion of a supersonic aircraft can be thought of as the linear superposition of small disturbances (i.e. sound waves) spreading out from its successive positions at the speed of sound.
In a homogeneous atmosphere, and thinking for simplicity of the aircraft as a point source in two dimensions, these disturbances form circular wave fronts centered at the successive positions of the aircraft.
Description of Sonic Boom
The wave fronts overlap and form an envelope, called the Mach envelope. In two dimensions the Mach envelope is a wedge, and in three-dimensions it is a cone, called the Mach cone. The semi vertical angle of the Mach cone is the Mach angle , where M is the ratio of the source speed to the sound speed and is called the Mach number.
All the sound is contained in the Mach envelope, and the envelope is the location of the sonic boom.
When an object passes through the air, it creates a series of pressure waves in front of it and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound, and as the speed of the object increases, the waves are forced together, or compressed, because they cannot "get out of the way" of each other, eventually merging into a single shock wave at the speed of sound. In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. Because directions around the aircraft's direction of travel are equivalent, the shock forms a Mach cone with the aircraft at its tip.
Since the boom is being generated continually as long as the aircraft is supersonic, it fills out a narrow path on the ground following the aircraft's flight path, a bit like an unrolling celebrity carpet and hence known as the "boom carpet". Its width depends on the altitude of the aircraft. The distance from the point on the ground where the boom is heard to the aircraft depends on its altitude and the angle a.
The later shock waves are somehow faster than the first one, travel faster and add to the main shockwave at some distance away from the aircraft to create a much more defined N-wave shape. This maximizes both the magnitude and the "rise time" of the shock which makes the boom seem louder
A larger and heavier aircraft must displace more air and create more lift to sustain flight, compared with small, light aircraft. Therefore, they will create sonic booms stronger and louder than those of smaller, lighter aircraft. The larger and heavier the aircraft, the stronger the shock waves will be.
Altitude determines the distance shock waves travel before reaching the ground, and this has the most significant effect on intensity. As the shock cone gets wider, and it moves outward and downward, its strength is reduced. Generally, the higher the aircraft, the greater the distance the shock wave must travel, reducing the intensity of the sonic boom. Of all the factors influencing sonic booms, increasing altitude is the most effective method of reducing sonic boom intensity.