Anatomy of a Wave

We can understand how electromagnetic radiation is transmitted through space if we appreciate that it involves waves. What is a wave? The first image that probably jumps to mind is that of ocean waves. And ocean waves do have some aspects in common with the kind of waves that we use to describe electromagnetic radiation. One way to think of a wave is that it is a way for energy to be transmitted from one place to another without any physical matter being moved from place to place. Or you may think of a wave as a disturbance that carries energy and that occurs in a distinctive and repeating pattern. A row boat out in the ocean will move up and down in a regular way as waves pass it. The waves do transmit energy to the shore (think of beach erosion), but the row boat will stay put.

That regular up-and-down motion that the rowboat experiences is called harmonic motion. But there are two important differences with electromagnetic radiation: The sources of waves are things on atomic scales (electrons and the nuclei of atoms), and no medium is required for electromagnetic waves to travel through space. The "pond" of space consists only of electric and magnetic fields, and photons of light are ripples in that ghostly pond.

Waves come in various shapes, but they all have a common anatomy. They have crests and troughs, which are, respectively, the high points above and low points below the level of an undisturbed state (for example, calm water). The distance from crest to crest (or trough to trough) is called the wavelength of the wave. The height of the wave— that is, the distance from the level of the undisturbed state to the crest of the wave—is its amplitude. The amount of time it takes for a wave to repeat itself at any point in space is its period. In other words, the period is the time between the passage of wave crests as seen by an observer in the bobbing row boat. The number of wave crests that pass a given point during a given unit of time is called the frequency of the wave. If many crests pass a point in a short period of time, we have a high-frequency wave. If few pass that point in the same amount of time, we have a low-frequency wave. The frequency and wavelength of a wave are inversely proportional to one another, meaning that as one gets bigger, the other gets smaller. High frequency radiation has short wavelengths.

Astronomer's Notebook

Recall from Chapter 5 that wave frequency is expressed in a unit of wave cycles per second, called the hertz, abbreviated Hz. Wavelength and frequency are inversely related; that is, if you double the wavelength, you automatically halve the frequency, and if you double the frequency, you automatically halve the wavelength. Multiply wavelength by frequency, and you get the wave's velocity. For electromagnetic radiation, wavelength multiplied by frequency is always c, the speed of light.

The parts of a wave. (Image from the authors' collection)

Undisturbed stmc

The parts of a wave. (Image from the authors' collection)

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