Moving wave source

A wave source travels to to the right at velocity $v$ while it emits waves that travel at a velocity $c$. The wavefronts are closer together in front of the source and they are farther apart behind the source. All of the wavefronts in the simulation are traveling at the same speed so where the wavefronts are closer together, an observer hears a higher frequency and where the wavefronts are farther apart, an observer hears a lower frequency. This is the Doppler effect. Try counting every time a wavefront reaches the left edge of the image and then count each time a wavefront reaches the right edge of the image. If the speed of the source is faster than the wave velocity $(\frac{v}{c} < 1)$, a conical shock wave is produced. The cone forms an angle $\theta=\sin^{-1}(\frac{c}{v})$ with the velocity vector of the source. The wavefronts add constructively on the cone so there is a loud noise.

It is relatively easy to drive a boat faster than the speed of water waves. The characteristic V-form wake behind a fast-moving boat is a shock wave.