A Note on the Sonic Bang Waveform of an Aircraft with Lift

Extract

It is well-known that, at large distances from the flight path, the waveform of the sonic bang from an aircraft, without lift at any rate, has the characteristic N-wave shape, as illustrated in Fig. 1. When we depict a waveform such as this we are stating what would occur at large distances in the absence of viscosity and other diffusive effects, such as turbulence. We know, of course, that in reality, because of these effects, the bow and stern shocks will be “softened”, i.e. the pressure jumps associated with them will not be instantaneous, but will have a finite, but small, “rise time”. However, this is not the matter under discussion. The essential feature of the N-wave illustrated in Fig. 1 is that the pressure jumps associated with the bow and stern shocks are equal, and that the positive and negative phases are of equal duration. The arguments for the waveform to take up this shape at large distances are put in a classical paper by Whitham.