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A square wave is a type of waveform where the signal has only two levels. The signal switches between these levels at regular intervals and the switch is instant. These qualities mean a graph of the wave over time will produce shapes with square corners. This waveform has practical uses in digital circuits and music.
Most waveforms follow a distinct pattern known as sine. Such waveforms switch back and forth between two levels gradually, such that a graph of the wave over time is a series of curves. The waves of the sea, light waves and sea waves all follow a sine pattern, as does the level of voltage in an alternating current system.
All other waveforms are categorized as non-sinusoidal waveforms. The most well-known of these, including the square wave, triangle wave and sawtooth waveforms also involve a signal which fluctuates between two levels. However, each of these behaves in a different way, characterized by whether the switch in either or both directions is instantaneous or gradual, how long the switch takes, and how long elapses between switches. The names come from the way a graph of the wave over time produces the appropriate shape. The instant changes of a square wave in both directions means the graph is shaped like the turret of a castle.
A square wave is fairly simple to generate artificially. This makes it particularly suitable for making sure different parts of a circuit are synchronized properly. The regular pattern of the wave acts as a timing device. It can also be used for synthesizing sounds in music. A sound wave which follows the square waveform pattern sounds similar to wind instruments such as horns, trombones and saxophones.
In reality, it's impossible to generate a perfect square wave. This is because there will be some physical limitations to the device used to generate it. For example, wiring used in the device's electrical circuits will have some resistance which delays the change in voltage levels.
The square wave is sometimes also known as the Rademacher function. That name comes from Hans Adolph Rademacher, a German mathematician who emigrated to the United States. As well as contributing his own work to mathematical study, he taught numerous students who also became leading academics and researchers in the field.