PERFECT WAVES

Surfers dream of riding perfect waves; engineers strive to synthesize them. For a surfer, a perfect wave might be “tubular,” “glassy,” and part of an “overhead set” in a swell at one of the beaches on the north shore of Oahu in February. In the mind of a communications engineer, a perfect wave is a sinusoid, also called a sine wave.
Even to a person who has never heard of the sine function, a sinusoidal waveform is easy to remember. An acoustic sinusoid makes an unforgettable noise. It focuses sound at a single frequency. A visual sinusoid has an unforgettable appearance. It concentrates light at a single wavelength. A perfect set of ocean waves can give a surfer an unforgettable thrill, and it, too, concentrates a lot of energy at a single wavelength.
Back in Chapter 13 the sine wave was represented by a child swinging an object around and around. As viewed from high above, the path of the object is a circle. As its trajectory is observed edge-on, the object seems to move toward the left, speed up, slow down, reverse, move toward the right, speed up, slow down, reverse, move toward the left again, speed up, slow down, and reverse. The actual motion of the object is circular and constant. Suppose that it takes place at a rate of one revolution per second. Then the object travels through 180° of arc every half second, 90° of arc every quarter second, 45° of arc every 18 second, and 1° of arc every 1360 second. A scientist or engineer will say that the object has an angular speed of 360°/s.