When we drop a stone in a pond, we see waves of water spreading over a distance.
Often did I see the geometry of the waves, it is mostly circular.
So no matter how the geometry of the stone is varied the waves seemed to me, a circular one.
Taking an irregular shaped middle sized stone and dropping in the water we see the phenomenon of circular waves spreading out, why is it that we always see circular one? If it's not always the case, please guide me so. Thanks in advance!
If the dimensions of the stone are comparable to or smaller than the wavelength of the ripple wave, then its geometry will have a diminishing effect on the circular shape of the wave.
Furthermore, any irregularities that may appear at the instant of impact will vanish with the propagation of the wave, as it propagates at the same speed in all directions. Suppose for example that the left side of the wave is preceding the right side by $5$cm on impact, this would seem as a great distortion, but after the wave propagates for $1$m for instance, a difference of $5$cm will be unnoticeable.
My guess is conservation of energy, a wavefront which followed the outline of an irregular shaped object would not be as low in energy as as it could be, so the water will act to counteract that. You could check this in two ways. Throw a large box shaped object in and see do the waves follow the outline or use a more viscous medium.
It's a very quick transition between the shape of the object and the shape of the water wave, which is difficult to observe.
The Green's function of the wave equation is a spherically expanding wave. In physical terms, this means that for an infinitesimally small disturbance (think for example of a small droplet falling into the water), you will get a spherically expanding wave.
When you throw an arbitrarily large stone in the water, you can think of it as a bunch of infinitesimally small stones added together. The resulting disturbance will then be the sum of all the spherically symmetric disturbances that are caused by all of the points on the stone's surface.
Of course, you are right in remarking that it is strange that the overall wave pattern still looks rather spherical. If we add a lot of spherically expanding waves together from the surface of the rock, wouldn't we expect the resulting wave to be as rigged as our original stone? There are two reasons why this isn't the case
First, the expanding spherical waves quickly form a smoother expanding spherical wave as they interfere with each other. The second reason (I think) is because of the adhesiveness of the water. When the stone falls in the pond the water sticks to its surface, causing the stone to look smoother as it is covered by a layer of water. This causes the resulting wave pattern to look smoother as well.
You can experiment yourself and you will probably see a clear distinction between spherical and elliptical stones.
