Ripples

By Chad Briedis

When you throw a stone into a calm piece of water it makes ripples.

Where do they go?

Obviously, they must have been unhappy where they were, so they go off to a better place...

"... the wave in a vessel runs several times from the circumference to its center and from the center to the circumference."

These words, translated from Renaissance Italian, represent the observations of Leonardo da Vinci, based on experiments he performed using a large circular vessel filled with water. Touching the water at the vessel's center produced a ripple that moved outward in an ever-widening circle to reach the rim, then was reflected back as a circle contracting toward the center. From the center, a circular wave would again propagate outward to renew the cycle.

The 72 pages of Leonardo's notebook contain a wide range of comments. For example, he studied how waves interact when they meet, noticing that two sets of circular ripples run into each other, overlap, then continue on without affecting each other's shape. He noted that "Water is of such agility that the motion of any wave ... will never be hindered by the motion of another wave which were to come its way,"Leonardo understood the difference between the motion of water and the motion of a wave on its surface. "Circular surface waves penetrate one another as impulses, not as a body of water, for the water does not move from its previous place on account of the waves, but only the impulses are transmitted,"

cancel each other out forming "quiet" regions where the water is not moving. These "quiet" regions map out a collection of hyperbolas.

This picture can be used to illustrate properties of hyperbolas including the fact that the difference of the distances from any point to the foci is a constant. Two vibrating pins form two sets of concentric circular waves in a flat glass "ripple tank". Where the two sets of circles intersect each other, they

Ripples.gsp

These circular waves consist of crests (high points in the wave) and troughs (low points in the wave). The length of an entire wave, one crest and one trough, is called the wavelength and is represented by the symbol lambda.

The circular water waves move out from their respective sources and overlap. In some spots, the two waves add together (constructive interference) to make a big wave. In other spots, the waves cancel each other out (destructive interference) and the water is still. In the places where the circular waves add constructively, double crests and double troughs are formed. These double crests and troughs appear as moving, bright regions on the screen. Where a crest from one source meets a trough from the other source, the waves cancel out and the water is still. These quiet regions, or nodal lines, appear as gray lines on the screen. In the figure below, the nodal lines are shown in black.

In the places where the circular waves add constructively, double crests and double troughs are formed. These double crests and troughs appear as moving, bright regions on the screen. Where a crest from one source meets a trough from the other source, the waves cancel out and the water is still. These quiet regions, or nodal lines, appear as gray lines on the screen. In the figure below, the nodal lines are shown in black.

                                A crest and a trough will meet only at points where the difference in distances from the point to the sources is 1/2 lambda, 3/2 lambda, 5/2 lambda, etc. That is, PS1-PS2 = (n-1/2)lambda, where n = 1,2,3,4,etc. This is just another way of stating the defining relationship for a hyperbola. In its usual form the definition states: a hyperbola is the locus of points in a plane such that for any point of the locus, the difference of the distance from two fixed points is a constant.

Check out the rippler---

Many wacko’s like to study ripples!