Physics hmk help...mach numbers and shock waves??? thank you!?

Question

The Concorde flies at Mach 1.3. What is the angle between the direction of propagation of the shock wave and the direction of the plane's velocity?

Answer 1

Per ref. 1, for speeds V equal to or greater than the speed of sound C (Mach No. M >= 1), the shock wave cone angle theta is defined as: sin(theta) = C/V = 1/M. I've had difficulty in getting a clear definition of the shock wave's propagation direction. At constant aircraft speed, the tip of the cone is located at the nose of the plane, and travels with the plane and thus could be considered to propagate forward. However it is often visualized as an infinite series of expanding spheres whose radial expansion rate is C and whose successive centers move at V. The tangent to all these spheres is a straight line along the length of the cone. This line can be considered to advance in a direction at right angles to itself, which would be at theta + 90 degrees. Ref. 2 discusses these aspects of its propagation.