How does Huygens' principle work with a wave pulse?

Question

Huygens' principle says that points on a wave can be thought of as the sources of new waves. This makes a lot of sense to me in the context of a moving wave and diffraction. However, in the context of a wave pulse, like a single stone being dropped into a pond, it feels as if Huygens' principle would predict that the circular wave pulse would reflect back in on itself.

When I drop a stone in water, it makes one ring coming out, but Huygens' principle would expect that that ring would send waves back towards the center where the stone hit. What's going on here?

Answer 1

With a compact wave pulse, Huygens’ Principle still holds, and points along the wave front acts as sources. On the advancing side of the pulse, the outgoing waves from different parts of the front interfere constructively. However, on the receding side, the waves have different phases and interfere destructively. That accounts for how the wave packet advanced into the quiescent region ahead of it but does not rebound back into the region behind.

(As a caveat, I should add that dropping a stone into a pond does not produce a clean outgoing pulse. A impulse source at a point produces an outgoing wave with no further disturbance behind it, but this does not occur in two dimensions. Behind the leading ripple produced by a thrown stone, there are still oscillations in the water’s surface after, which makes the analysis via Huygens’ Principle quite a bit more complicated.)