The head-on encounter of a plane shock, of any strength, with a solid corner of angle π - δ is investigated mathematically, when δ is small, by a method similar to that of part I. The incident shock is found to be reflected from each face as a straight segment, the two segments being joined by a shorter curved portion. Behind each straight segment is a region of uniform flow, the two regions being joined by one of non-uniform flow, bounded by arcs of a circle with centre at the corner, which expands at the local speed of sound, and by the shock, which is curved only where intersected by the said circle. The pressure is approximately equal in the two regions of uniform flow, but is less in the region of non-uniform flow between them; and it is found that if the deficiency of pressure therein, divided by the angle δ and by the excess of pressure behind the reflected shock over that of the atmosphere, be plotted at points along the solid surface, after the incident shock has travelled a given perpendicular distance beyond the corner, then the curve is independent of δ and of the precise angle of incidence of the shock, and changes remarkably little in the whole range of incident shock strengths from 0 to ∞ (see figures 5 to 8). It is suggested that some of the above qualitative conclusions may be true even if δ is not small. The case δ<0, when the corner is concave to the atmosphere, is also considered. Shock patterns are found in cases when the incident shock has already been reflected from one, or both, walls before reaching the corner (figures 9 to 11).
Photoacoustic–ultrasonic dual-mode microscopy with local speed-of-sound estimation
