Image: The Mach cone is a relevant image of the concept of shock wave and sound barrier. When the plane exceeds Mach 1, the waves fall into a cone with the plane as its apex. The boundary between the mach cone and the exterior forms a hyperbola that advances with the plane. The intensity of the bang is the result of the abrupt change in pressure when the air pressure suddenly returns to its natural average balance. This implosion of the wave on itself causes the bang.
Credit: FA-18 Hornet breaking the sound barrier on July 7, 1999 by Ensign John Gay, US Navy
Shock wave
Before explaining the Cherenkov effect it is necessary to understand the phenomenon that creates the shock wave produced behind an aircraft that exceeds the speed of sound (≈340 m/s).
When the speed of the plane is less than the speed of sound, sound waves propagate around it in all directions. These concentric spheres of air pressure increase their radius by 340 meters every second and the plane is still inside the wavefront. Thus, the sound waves produced by the collisions of the air molecules move faster than the plane and their energies dissipate slowly with the square of the distance (i=p/4πr2).
But, as the speed of the plane increases, the waves in front of it get closer to each other and settle more and more, while those behind stretch out. This effect of sound frequencies expanding and contracting is the cause of the Doppler effect (the sound of approaching sound objects seems higher pitched!).
The intensity of sound waves can add up like the heights of waves can add up when they meet. As long as the plane moves slower than the sound waves it creates, the waves remain circumscribed within each other without their energy adding up.
But when the plane reaches the speed of sound, while generating new waves from its current position, the waves which have the same phase come together, accumulate in front of it and the pressure rises suddenly forming a shock wave. Then the pressure decreases along the plane to rise again suddenly at the level of the tail of the plane. These two overpressures cause two sonic booms so close together that our ear only hears one. This bang is not heard by passengers because the pressure shock behind the plane cannot catch up with the plane. The shock waves then propagate in a cone called the Mach cone.
When the speed of the plane exceeds Mach 1, it crosses in an instant the compressed air barrier which had formed in front of it, this is what is called the sound barrier. The shock wave produced causes the surrounding air to undergo sudden variations in pressure and temperature. It happens that the temperature of the air drops below the dew point, the water vapor contained in the air then condenses into fine droplets forming a cloud which accompanies the plane in its supersonic flight as in the photo.
Explanation of the Cherenkov effect
Image: The bluish luminosity of the water in the spent fuel cooling pools of nuclear power plants is generated by the Cherenkov effect.
The speed of light in vacuum (299792 km/s) is the maximum speed of energy movement. But the speed of light in water (225563 km/s) can be exceeded, which makes the Cherenkov effect possible.
Credit: Cherenkov radiation in the core of the Advanced Test Reactor, Idaho National Laboratory.
Cherenkov light, by Russian physicist Pavel Tcherenkov (1904-1990), is a flash of light produced by a particle with an electrical charge as it moves through a material medium (such as water or air) with a speed greater than the speed of light in this medium. The speed of light in vacuum is always greater than this.
The analogy between the Cherenkov effect and the supersonic shock wave is easy to imagine.
An airplane moving faster than sound through the air creates a shock wave on which all sound waves meet. The correspondence with the Cherenkov effect is made by replacing the plane by a charged particle and the sound by light.
In a material medium like water or air, light travels at a speed c1 = c/n.
c = speed of light in vacuum
n = refractive index of the medium always > 1 (examples: air=1.0003, water=1.333, optical fiber=1.5, diamond=2.41)
A charged particle can move in this medium at a speed v greater than c1 but remains less than c, which does not contradict the special theory of relativity.
What explains this blue radiative emission in the water?
The charged particle interacts throughout its trajectory with the medium it crosses. During its journey through the water, it temporarily disrupts the atoms it encounters. In other words, the electrons deviate from their initial position, then return to their place. Thus, each atom encountered by the particle returns the absorbed energy and becomes an emitter of radiation. All the waves emitted by each of the atoms are superimposed in a disordered way, they present different phases, so much so that their sum cancels out.
However, the speed in water of the charged particle, which can be assimilated to the supersonic plane, is faster than the speed of the wave emitted by each atom in the water. When the particle exceeds the speed of light in the medium, all the waves are found on the same phase and therefore add constructively as in the case of the supersonic shock wave. This phenomenon then causes a wave front analogous to the sound barrier in the Mach cone. A sudden transition then occurs over the entire trajectory of the particle, ie 10 billion times per meter. The Cherenkov effect manifests itself, all along the route, by the emission of a light wave at all wavelengths, with a predominance in blue and ultraviolet.
These flashes explain the blue light in the spent fuel cooling pools of nuclear power plants. It is due to the energetic electrons emitted by the radioactivity which reach speeds greater than that of light in water.
Cherenkov detectors are located in large tanks of water and are used to detect very high energy particles (Antarctic Muon and Neutrino Detector Array, Super-Kamiokande).
Cherenkov light is also involved in the detection of neutrinos produced in nuclear reactions at the core of the Sun (Sudbury Neutrino Observatory).
The astronauts of the Apollo missions had all complained of phosphenes during their missions. It was discovered that these luminous visual disturbances were due to the Cherenkov effect. Solar wind particles passing through the liquid of the eyeballs produce phosphenes. Such phosphenes also occur on Earth, at the rate of one or two on average per person per year.