Final answer:
The hourglass shape of the sound beam is caused by the constructive and destructive interference of sound waves, particularly when a source moves faster than the speed of sound, creating a shock wave known as a sonic boom.
Step-by-step explanation:
The hourglass shape of the sound beam is typically a result of constructive and destructive interference of sound waves. In instances where a source of sound moves faster than the speed of sound, spherical waves are spread out from the point where they are emitted, and the source can move ahead of these waves. Constructive interference occurs when waves are in phase, and this can create a shock wave known as a sonic boom. This is evident in the angle and shape of the shock wave, which is determined by the speed of the source relative to the speed of sound, displaying a clear hourglass or cone-like shape in three dimensions. The faster the source moves, the smaller the angle becomes, which is represented by the geometric relationship where the sine of the angle equals the inverse of the Mach number.