3.7.13 | revision #20125 | Savchenko Solutions

Statement

3.7.13. The region of increased pressure at the boundary of the medium propagates to the right with a speed $$v$$ greater than the speed of sound $$c$$ in the medium. What is the wave front in the medium? What is the direction of its propagation?

Solution

Let $$A$$ and $$B$$ be previous and current positions of the source and $$C$$ be a point on the wavefront. Then, $$AC/AB=c/v$$ , so the envelope of emitted spherical waves is the surface of a cone. The angle between the wavefront and the direction of the source is $\alpha=\arcsin(c/v)$ .

Answer

A conical wavefront making an angle $\alpha=\arcsin(c/v)$ with the direction of the source.