falling sand curve

Imagine a basket of sand, oscillating harmonically on a string. When there is a hole in the basket, so that the sand pours down on the ground, a dune of sand emerges. We admit that the amount of falling sand is constant with time, and we neglect the horizontal velocity of the sand ¹⁾. Then the profile of the sand dune has a curve as shown in the drawn curve.

Therefore I call the curve the falling sand curve.

notes

1) It may be more proper to do the experiment with light instead, so that we can neglect the horizontal movement of the falling property.