As shown in the drawing, the half-angle of the shock wave cone generated by a supersonic airplane is 45°. What is the speed of the plane relative to the speed of sound?
Solution 7P The relation between Mach number and half-angle is sin = 1/M , where M is the Mach number and is the half angle. Given that, = 45 0 0 Therefore, the Mach number M = 1/sin 45 M = 1/(1/ 2) M = 2 If the sound speed is assumed to be 340 m/s, then the speed of the plane relative to the speed of sound = 340 m/s × M = 340 m/s × 2 480 m/s Therefore, the approximate speed of the plane will be 480 m/s.