Oscillations and Waves > Wave propagation > Problem 3.7.15

Statement

When an airplane flies at subsonic speed, the noise of its engines can be heard on the ground. When a plane flies by at supersonic speed, you will first hear a loud popping noise and then the noise of the engines. What is it related to?

Solution

Since the speed of the plane exceeds the speed of sound, a spherical wave emitted at a later time is not contained in another spherical wave emitted at an earlier time. As a result, an envelope (i.e. shock wave) of these spherical waves is formed in the shape of a cone. In the figure, the shock wave (red) reaches an observer at as a loud popping noise before a spherical wave (blue) emitted from arrives as the noise of the engines a short moment later, by which time the shock wave (blue) has already passed the observer.

Answer

See the solution.