The waves move at a characteristic speed which is set by their wavelength and the frequency, v_s = \lambda\vu. If the source itself is moving at a speed close to v_s, then it nearly keeps pace with its own spherical wave fronts as shown in the top diagram below.
The second diagram shows what happens if the speed of the source exceeds v_s. In this case, when the source S was at position S_1 it generated wavefront W_1, and at position S_6 it generated W_6. All the spherical wavefronts expand at the speed v_s and bunch along the surface of a cone. In the case of a wave source in a fluid like water or air, the cone signifies a shock wave and is referred to as the Mach cone. The surface of this cone has half-angle \theta, and is tangent to all the wave fronts. A similar effect occurs for light when an electrically charged particle traverses a dielectric medium at speeds that are greater than those of light in that medium. In this case, the electric and magnetic fields associated with a rapidly moving charge excite the atoms of the medium. The excited atoms emit part of their light in the form of a coherent wavefront of radiation at fixed angle with respect to the trajectory of the charged particle as shown below.
To be precise, this radiation, named Cerenkov radiation after its discoverer, is produced whenever the velocity \beta c of the particle exceeds c/n, where c is the speed of light in a vacuum, n is the index of refraction of the medium traversed by the charge, and beta is the usual relativistic term given by the expression
beta = {1\over\sqrt{1 - (v/c)^2}} if v is the velocity of the charge. For most cases, energies are high enough for us to assume beta~ 1. From the diagram above, we can see that the light cone formed in Cerenkov radiation has a value {\rm cos}\theta = {ct/n\over\beta c t} = {1\over\beta n} The radiation appears as a continuous spectrum. In a dispersive medium, both n and \theta are functions of the frequency of radiation. The number of photons at a particular frequency or wavelength, as it turns out, is proportional to 1/\lambda^2. Therefore, the smaller the wavelength (or conversely, the higher the frequency), the more photons you get. This means that, in the visible range, blue light predominates over all other colors. The blue glow that emanates from the water in which highly radioactive nuclear reactor fuel rods are stored is caused by the Cerenkov effect. For fuel rods, much of the radiation they emit is in the form of high energy electrons. The electrons travel through the water at a velocity greater than that of light in water and hence cause the characteristic ``Cerenkov glow''. The importance of the Cerenkov effect as a scientific tool lies in the connection between particle speed and angle between momentum direction and radiation emission. A measurement of the angle $theta$ described above provides a direct measurement of \beta c. If its assumed that the particle we are dealing with is very light (this is the case for electrons and positrons), then \beta is very close to 1 for almost all cases and the angle can be used to determine the direction of the electron or positron. By measuring the trajectory of both an electron and positron from a single gamma ray, we can determine the momentum, direction and magnitude, of the gamma ray itself. This is our goal for the balloon project.