Perfect Waves:

Surfers vision of riding perfect waves; engineers strive to produce them. For a surfer, a perfect wave may be "glassy", "tubular," and part of an "overhead set" in a swell at one of the beaches on the north shore of Oahu in February. In the brain of a communications engineer, a perfect wave is a sinusoid, also termed as sine wave.

 Even to a person who has never listened to of the sine function, a sinusoidal waveform is simple to keep in mind. An acoustic sinusoid makes a memorable noise. It focuses sound at a single frequency. The visual sinusoid has a memorable appearance. It concentrates light at a single wavelength. The perfect set of ocean waves can provide a surfer a memorable thrill, and it, too, concentrates a lot of energy at a single wavelength.

The sine wave was symbolized by a child swinging an object around and around. As seen from high above, the path of the object is a circle. As its trajectory is noticed edge-on, the object appears to move to the left, speed up, slow down, reverse, move to the right, speed up, slow down, reverse, move toward the left again, speed up, slow down, & oppose. The real motion of the object is constant and circular.

Assume that it occurs at a rate of one revolution per second. Then the object travels via 180° of arc every half second, 90° of arc in every quarter second, 45° of arc each and every 1/8 second, and 1° of arc every 1/360 second. The scientist or engineer will say that the object has an angular speed of 360°/s.