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Where does the Mach cone that forms around a flying plane come from?
You have certainly already seen in photos showing military aircrafts passing the sound barrier that there was sometimes a cone that formed around them. And you might have wondered where it could come from. It is weird, isn't it? Here is a brief explanation of what is behind this nice phenomenon.

Wave propagation

First of all, you should know that the sound is a variation of pressure which propagates in form of a wave at a speed logically called the speed of sound. This speed is not constant as we could think and depends on the fluid in which the sound is propagating (mainly nature of the fluid, temperature and pressure).

When an airplane moves, it displaces air and that produces waves, in the same way that a stone thrown into water. Waves propagate in all directions and at the same speed forming increasingly large circles. In the air, the speed of these waves is the speed of sound, that is why these waves are called acoustic waves. In aeronautics, the speed of sound is a speed unit commonly used under the term Mach number.

Supersonic speed

If the airplane causing these waves flies at a speed lower than the speed of sound, that is to say less than Mach 1, we say that it flies at a subsonic speed. If it moves at a speed close to Mach 1, the waves do not exceed the front of the airplane and we say that it flies at a transonic speed. Once it exceeds Mach 1, we say that it flies at a supersonic speed.

  • Subsonic speed:
  • \[\mbox{speed of the object} \leq \mbox{speed of sound} = \mbox{Mach 1}\]
  • Transonic speed:
  • \[\mbox{speed of the object} \approx \mbox{speed of sound} = \mbox{Mach 1}\]
  • Supersonic speed:
  • \[\mbox{speed of the object} \geq \mbox{speed of sound} = \mbox{Mach 1}\]

Mach cone

When an airplane (or any other object) moves at a speed larger than the speed of sound (supersonic speed), it moves forward faster than the waves that it generates by its moving. That creates an accumulation of waves that generates a strong pressure in the air. It produces what we call shock waves, it means a sudden change of the speed and the pressure that starts mainly from the airplane's nose and moves away (in a continuous way) from the airplane still moving. These shock waves generated by the contact between the structure of the airplane and the propagating waves form a cone of revolution around the airplane, the apex of which is at the foremost point of the airplane. This cone, called in aeronautics "Mach cone", delimits the air flow disturbed by the object inside this Mach cone (which is supersonic) from the undisturbed air flow at the outside of the Mach cone (which is subsonic).

Subsonic speed : the waves precede the airplane.

Transonic speed : the airplane reaches the sound of speed (Mach 1).

Supersonic speed : the airplane is ahead of the acoustic waves.

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