Cross sectional view of two Mach cones
The sonic boom is the noise from two shock waves which a supersonic aircraft continuously generates as it flies supersonically through the atmosphere. As shown schematically in the sketches, the first shock forms at the nose of the aircraft (large arrow in the left sketch) and the second near the tail.
| Cross sectional view of two Mach cones |
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You might be interested in seeing more about how waves are generated at supersonic speed. (Compare with how waves are made by a stationary object; and with other kinds of waves.)
The shocks form two cones, one with its tip at the nose of the aircraft and the other at the rear. They start out very close together (one body length apart, which means they are separated by much less than 0.1 sec), but, as they propagate the long distance to the Earth's surface, they spread apart, and the time between them gets as large as 1 sec. That's why you can actually hear two closely-spaced booms. The longer the aircraft's fuselage and the higher it is flying, the easier it is to distinguish the two shocks.
The aircraft at two different instants of time is shown in the left sketch. The dashed line is the flight path. The lower half of the shock cones and a little bit of the upper are indicated in cross section. The portion of the wave front that you hear on the ground was actually generated before the aircraft gets directly over you, the wave path to the ground being shown by the line with small arrows.
In getting to the ground, the portion of the wave front that gets to you propagates normal to itself at the speed of sound a, so the delay from the aircraft to you is given by the propagation distance along the line with arrows, divided by the sound speed a. The distance is, ignoring the small spreading of the fronts, approximately h cos µ, where h is the altitude and µ is the angle shown, known as the "Mach angle." The normal propagation property determines the Mach angle µ in terms of the Mach number of the aircraft M = u/a, where u is the flight speed. In fact, the magnitude of the Mach angle is µ = arcsin(1/M).
Measuring the time between two observations of the boom on the ground directly gives the flight speed u of the aircraft, as suggested by the left sketch.
A typical sonic boom pressure amplitude from a supersonic aircraft is about 2 psf (pounds per square foot) = 0.014 psi = 95 Pa. In acoustics this would be measured as 133 dB (deciBel), which is very loud.