What Happens When Something Outruns Its Own Sound? A Pressure Front
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When an object moves faster than the disturbances it creates can travel, those disturbances pile into a surface across which pressure changes almost instantly. That surface explains sonic booms, supersonic flight and a good deal of astrophysics.
How the pile-up happens
An object moving through air pushes it aside, and that push travels outwards as a pressure disturbance at the speed of sound. While the object moves more slowly than that, the disturbances run ahead of it and the air gets advance warning, flowing smoothly around what is coming. Once the object matches or exceeds that speed, the disturbances can no longer outrun it, so each new one is emitted closer to the previous one and they accumulate along a surface. Across that surface pressure, density and temperature change over a distance of a few molecular mean free paths, which is close enough to instantaneous that it is treated as a discontinuity in the mathematics.
What is discontinuous across it
The quantities change abruptly and the changes are linked:
- •Pressure rises sharply, which is what makes the passage audible and damaging
- •Density rises, compressing the gas into a thinner layer
- •Temperature rises, sometimes by enough to dissociate or ionise the gas
- •Flow speed relative to the front drops from supersonic to subsonic
- •Entropy increases, which means the process is irreversible and dissipates energy
- •The relations between these are fixed by conservation of mass, momentum and energy
Why a boom is heard on the ground
A sonic boom is not a single event at the moment of crossing the sound barrier, which is the most persistent misconception about it. An aircraft in sustained supersonic flight trails a conical pressure front continuously, and that cone sweeps across the ground behind it, so anyone within the swept region hears a boom as the cone passes them. The aircraft has been supersonic for a long time before and after. Two fronts usually reach the ground, one from the nose and one from the tail, which is why the sound is a double bang rather than one. The overpressure is modest in absolute terms and the suddenness is what makes it startling and what cracks plaster and glass.
Designing around it
Supersonic flight is mostly a problem of managing these fronts and the engineering reflects that. Wings are swept back so the airflow crossing them behaves as though it were slower, which delays the formation of strong fronts on the wing itself. Bodies are made slender and pointed, since a blunt shape produces a detached front standing ahead of it that costs enormous drag. Engine intakes are shaped to slow incoming air below the speed of sound before it reaches the compressor, which is done with carefully positioned surfaces and movable ramps, and getting it wrong destroys the engine. Drag rises steeply near the speed of sound, which is why the transition needs a surge of thrust. Current research on quieter supersonic aircraft aims to shape the airframe so the fronts reaching the ground merge into a soft thump.
Where else they occur
The same physics operates wherever something moves faster than disturbances can propagate in the medium. Explosions generate a blast front expanding from the detonation, which is the mechanism by which an explosion damages things at a distance rather than the heat or the fragments alone. A bullwhip cracks because the tip exceeds the speed of sound. Supernova remnants drive fronts through interstellar gas for thousands of years, heating it to millions of degrees and generating the X-ray emission by which the remnants are found. The solar wind meeting a planet's magnetic field forms a standing front ahead of it. Water has an analogue in the hydraulic jump, visible where a fast shallow flow suddenly deepens, which behaves mathematically in much the same way.
The takeaway
Disturbances travelling at the speed of sound cannot outrun an object moving faster, so they accumulate into a surface across which pressure, density and temperature jump almost instantly. A supersonic aircraft trails such a cone continuously, and the boom is heard wherever that cone sweeps rather than at the moment of crossing. Explosions, supernova remnants and the solar wind all produce the same structure.