What are harmonics and what kind of wave creates them

[Peter Walker]

Harmonics are multiples of any given frequency. For example if you have a frequency of 1000 Hertz then 2000 Hertz is the second harmonic of it, 3000 Hertz is the third harmonic etc. Normally harmonics are integer multiples - although they don't absolutely have to be. Fractional harmonics are very rare however.

Sub harmonics are divisions of any given frequency. So 500 Hertz may be considered to be a subharmonic of 1000 Hertz. But the definition of subharmonics is more complicated than straight harmonics and we don't normally need to consider them.

Harmonics are sometimes also called "overtones" and subharmonics are sometimes called "undertones".

A sine wave is considered to be the purest form of wave - it contains only one frequency and no harmonics. There is a mathematical theorem called Fourier's theorem that says that any wave of any shape or form or harmonic content may be made up just by using lots of different sine waves. Engineers use Fourier series (and other mathematical tools called Fourier transforms) to work out how to break any non-sine wave into its harmonics for analysis. The harmonic content of any wave is called its spectrum.

There is a simple rule that allows one to work out if any wave contains odd or even harmonics - quite simply, you draw a horizontal line through the centre of the wave, and if the wave is symmetrical above and below the line, then the wave contains only odd harmonics. If the wave is not symmetrical in this way then it must contain even harmonics (but may also contain odd harmonics at the same time).

Any wave, no matter what the shape or form or frequency that is not a pure sine wave contains harmonics.

A square wave is a wave that is basically rectangular in shape. The true definition of a square wave is that the time the wave is low is equal to the time the wave is high (see Duty cycle for more on this). A square wave consists of a fundamental (its basic frequency) and an infinite number of ODD harmonics. For example, a 1000 Hertz square wave will contain a 1000 Hertz sine wave, plus a 3000 Hertz sine wave, plus a 5000 Hertz sinewave and so on right up to infinity. Each of the harmonics will be reduced in amplitude (size or intensity) by the ratio of their harmonic number - what this means is that the 3rd harmonic (3000 Hertz in the example above) will be only 1/3 rd of the amplitude or strength of the fundamental, 1000 Hz. The 5th Harmonic (5000 Hertz) will be 1/5th of the amplitude or strength of the fundamental.

A triangle wave is like a straight ramp (diagonal) that goes up and then comes down again at the same rate (also diagonal) - imagine a triangle! It's symmetrical. A triangle contains only ODD harmonics just like a square wave except that the harmonics drop off in intensity much more rapidly than a square wave.

A sawtooth wave looks like one of the teeth of a saw! It's a straight ramp (diagonal) that goes up and then suddenly drops straight down to zero. It is not symmetrical. A sawtooth contains both ODD and EVEN harmonics. The harmonics drop off by the ratio of their harmonic number (like the square).

A damped wave (for example a damped sine) is a wave that starts off at one level and decreases in intensity over time.

There are many other wave forms and shapes possible but these are the main ones encountered in Rife type work.