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# Intangible Waves Help

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## Introduction

The easiest waves to think about are the ones we can see and feel. Water waves are the best example. If you sit on a beach where swells are rolling in, you can feel their force and rhythm. Prehistoric humans no doubt spent hours staring at the waves on lakes and oceans, wondering where they came from, why they were sometimes big and sometimes small, why they were sometimes smooth and other times choppy, why they sometimes came from the west and other times came from the north, and why they sometimes moved with the wind and other times moved against the wind.

Imagine a child, 100,000 years ago, dropping a pebble into a pond or watching a fish jump and noticing that the ripples emanating from the disturbance were just like ocean swells, except smaller. This must have been a revelation, but it was nothing compared to the discoveries scientists would later make with the help of instruments, mathematics, and a fascination with the intangible.

## Electromagnetic Waves

Think about the electromagnetic (EM) fields generated by wireless broadcasting. In the journal of cosmic history, these waves have existed in our corner of the universe for only a short while. Our galaxy is ancient, but television programs have been airing for less than 2 × 10 −8 of its life.

Television waves don’t arise directly out of nature. They are manufactured by specialized equipment invented by a particular species of living thing on the third planet in orbit around a medium-small star. Perhaps such waves are generated by other species who live on other planets in orbit around other stars. If so, we haven’t heard any of their signals yet.

## Gravitational Waves

Some scientists think gravitational waves exist and that the fabric of space is swarming with them, just as the sea is filled with swells and chop. There’s a theory to the effect that the evolution of the known universe is a single cycle in an oscillating system, a wave with a period unimaginably long.

How many people walk around thinking they are submicroscopic specks on a particle in an expanding and collapsing bubble in the laboratory of the heavens? Not many, but even to them, gravitational waves, assuming that they exist, are impossible to see with our eyes and difficult to envision even with the keenest mind’s eye because gravitational waves are four-dimensional.

## 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.

A sine wave can be 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 1/8 second, and 1° of arc every 1/360 second. A scientist or engineer will say that the object has an angular speed of 360°/s.

## Graphing A Sine Wave

Suppose that you draw a precise graph of the swinging object’s position with respect to time as seen from edge-on. Time is plotted horizontally; the past is toward the left, and the future is toward the right. One complete revolution of the object appears on the graph as a sine wave. Degree values can be assigned along this wave corresponding to the degrees around the circle (Fig. 17-1).

Fig. 17-1 . Graphic representation of a sine wave as circular motion.

Constant rotational motion, such as that of the object on the string, takes place all over the universe. The child whirling the object can’t make the object abruptly slow down and speed up, or instantly stop and change direction, or revolve in steps like a ratchet wheel. However, once that mass is moving, it doesn’t take much energy to keep it going. Uniform circular motion is a theoretical ideal. There’s no better way to whirl an object around and around. A sinusoid is a theoretical ideal, too. There’s no better way to make a wave.

Practice problems of these concepts can be found at: Wave Phenomena Practice Test

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