If an object moves faster than the waves that it generates in the medium, it excites a trail of shock waves radiating behind it.

Any object, moving in a material environment, excites diverging waves in it. An airplane, for example, affects air molecules in the atmosphere. From each point in space, where the plane has just flown, an acoustic wave begins to diverge in all directions at an equal speed, in strict accordance with the laws of wave propagation in the air. Thus, each point of the trajectory of an object in the medium (in this case, an aircraft) becomes a separate source of a wave with a spherical front.

When the aircraft moves at subsonic speeds, these acoustic waves propagate like ordinary concentric circles through the water, and we hear the familiar drone of a flying aircraft. If the plane is flying at supersonic speed, the source of each next wave is removed along the trajectory of the plane by a distance exceeding that which by this moment the front of the previous acoustic wave had covered. Thus, the waves no longer diverge in concentric circles, their fronts intersect and mutually amplify as a result of resonance occurring on a line directed at an acute angle backward with respect to the trajectory of motion. And this happens continuously during the entire flight at supersonic speed, as a result of which the aircraft leaves behind a diverging train of resonant waves along the conical surface, at the top of which the aircraft is located. The strength of sound in this conical front is much greater than the usual noise emitted by an aircraft in the air, and this front itself is called a shock wave. Shock waves, propagating in the environment, have a sharp and sometimes destructive effect on material objects that meet in their path. When a supersonic aircraft is flying nearby, when the conical front of the shock wave reaches you, you will hear and feel a sharp, powerful pop, similar to an explosion – sonic boom… Do not be afraid, this is not an explosion, but the result of a resonant superposition of acoustic waves: in a fraction of an instant you hear all the total noise emitted by the aircraft over a sufficiently long period of time.

The cone of the shock front is called Mach cone… Angle φ between the generatrices of the Mach cone and its axis (see figure) is determined by the formula:

sin φ = u/v

Where u – the speed of sound in the medium, v – aircraft speed. The ratio of the speed of a moving object to the speed of sound in a medium is called Mach number: M = v/u… (Accordingly, sin φ = 1 /M.) It is easy to see that for an airplane flying at the speed of sound, M = 1, and at supersonic speeds, the Mach number is greater than 1.

Shock waves aren’t just about acoustics. For example, if an elementary particle moves in a medium with a speed exceeding the speed of propagation of light in this medium, a shock light wave (cm. Cherenkov radiation). Physicists today use this radiation to identify elementary particles and determine the speed of their movement.

See also:
Cherenkov radiation
Ernst MAX
Ernst MAX
Ernst Mach, 1838-1916

Austrian physicist. Born in Moravia, in Turas (now Turani, Czech Republic), he received his education from his father, who paid special attention to the development of both theoretical knowledge and practical skills in his son. He received his doctorate at the University of Vienna in 1860, where from 1895 until the end of his life he was a professor of the history of science. Mach earned the main recognition precisely for his works in the field of philosophy and the history of science, but his contribution to psychology and physics is also important. In addition to studying shock waves, the scientist formulated one of the most important postulates of theoretical mechanics, called the “Mach principle” and stating that the inertia of an object comes from its gravitational interaction with the total mass of the rest of the Universe.

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