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Frequency and Wavelength
For any kind of wave, frequency and wavelength are inversely related: The higher the frequency, the shorter the wavelength. Radio waves are part of the electromagnetic spectrum, as are microwaves, light and X-rays. To find the wavelength of any kind of electromagnetic radiation, divide the speed of light by the frequency. Radio waves, being of relatively low frequency, have long wavelengths, ranging from a few centimeters to hundreds of meters long.
Waveshape
Radio waves have a simple sinusoidal waveshape. The wave begins at a point of zero energy, gradually increases to a maximum, decreases back to zero, then to a negative maximum, and back to zero again. Each zero point is called a node; the maximum points are antinodes.
Fractional Wavelength
The most efficient antennas are tuned to one particular frequency, and are one wavelength long. For radio waves of many meters, this is a problem: You cannot fit a 300-meter antenna in a car or portable radio. In most cases, using an antenna of one-half or one-quarter wavelength is nearly as efficient as a full-wave one. Even a 75-meter antenna is too much to ask of a pocket radio, however. For consumer music, news and sports radio, electronics designers made compromises to make a compact design work for the average person.
Efficiency
Efficiency becomes most important with weak signals. Commercial radio broadcasters put out powerful signals so antenna efficiency is less important. Also, a decent radio receiver boosts the electrical signals from the antenna. Because of the combination of strong broadcast signals and radio-signal amplification, a standard radio gets by with a short, simple antenna. At least for commercial radio, convenience and portability take precedence over efficiency.