Solved: An airplane flying faster than the speed of sound sends out sound waves that
Chapter 5, Problem 59(choose chapter or problem)
An airplane flying faster than the speed of sound sends out sound waves that form a cone, as shown in the figure. The cone intersects the ground to form a hyperbola. As this hyperbola passes over a particular point on the ground, a sonic boom is heard at that point. If u is the angle at the vertex of the cone, then sin u 2 = 1 m , where m is the Mach number for the speed of the plane. (We assume m 7 1.) The Mach number is the ratio of the speed of the plane to the speed of sound. Thus, a speed of Mach 1.4 means that the plane is fying at 1.4 times the speed of sound. In each of the following exercises, u or m is given. Find the other value (u to the nearest degree and m to the nearest tenth as applicable). m = 5 4
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