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| - In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc, as well as f itself. The harmonics have the property that they are all periodic at the signal frequency. Also, due to the properties of Fourier series, the sum of the signal and its harmonics is also periodic at that frequency. The fundamental frequency is the reciprocal of the period of the periodic phenomenon.
- Accoustic theory, developed originally by Helmholz in the 19th century, holds that all periodic (repeating) waveforms, of whatever shape, are made up of a mix of sine waves of various frequencies. For most musical instruments and many natural sounds, the frequencies of these sine waves obey the harmonic series. A harmonic series consists of a sine wave at a particular frequency (referred to as the fundamental), and a series of higher tones which are referred to as harmonics. Each harmonic is a positive integer multiple of the frequency of the fundamental; the second harmonic is twice the fundamental’s frequency, the third harmonic is 3x the fundamental, and so on. Usually, the frequency of the fundamental determines the pitch of the note that the listener perceives, and the strength of the
- Harmonics are distorted signals or wave forms. Harmonics as voltages or currents that at frequencies are a multiple of the fundamental frequency. In most systems, the fundamental frequency is 60 Hz. Therefore, harmonic order is 120 Hz, 180 Hz, 240 Hz and so on. (For European countries with 50 Hz systems, the harmonic order is 100 Hz, 150 Hz, 200 Hz, etc.) When most electrical engineers design the building's wiring, they usually leave the sizing of the neutral conductor to the dictates of NEC. In most cases, the installed neutral is the same size as the phase conductors.
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| abstract
| - In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc, as well as f itself. The harmonics have the property that they are all periodic at the signal frequency. Also, due to the properties of Fourier series, the sum of the signal and its harmonics is also periodic at that frequency. Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics. Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are sometimes perceived as unpleasant. The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as inharmonics. Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics. The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted: In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g. recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found half way down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics. Harmonics may be either used or considered as the basis of just intonation systems. Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowing technique halfway between hitting and bowing the strings. Composer Lawrence Ball uses harmonics to generate music electronically. The fundamental frequency is the reciprocal of the period of the periodic phenomenon.
- Accoustic theory, developed originally by Helmholz in the 19th century, holds that all periodic (repeating) waveforms, of whatever shape, are made up of a mix of sine waves of various frequencies. For most musical instruments and many natural sounds, the frequencies of these sine waves obey the harmonic series. A harmonic series consists of a sine wave at a particular frequency (referred to as the fundamental), and a series of higher tones which are referred to as harmonics. Each harmonic is a positive integer multiple of the frequency of the fundamental; the second harmonic is twice the fundamental’s frequency, the third harmonic is 3x the fundamental, and so on. Usually, the frequency of the fundamental determines the pitch of the note that the listener perceives, and the strength of the various harmonics determine the timbre and character of the note. (When a guitarist plays a “harmonic” at the 12th fret, the guitarist is effectively demonstrating this theory; the finger touched lightly to the string mutes the fundamental and some of the odd-numbered harmonics, changing the character of the normal string sound.) Understanding of the harmonic series, and its effect on the ear, is essential to determining why a particular sound has the tonal characteristics that it has. Some well-known waveform types can be precisely described mathematically in terms of harmonic series; for example, a square wave is made up of a fundamental and all odd-multiple harmonics mixed in a certain proportion. Most synthesis techniques involved altering the harmonics of a waveform in some form. Subtractive synthesis, the method used by most analog synthesizers, starts with a certain waveform (such as a square wave) and uses filters to increase or decrease the strength of certain harmonics, altering the timbre. Additive synthesis takes the opposite approach; it starts with a sine-wave fundemental and then adds other sine waves at the harmonic frequencies, at various strengths, to build up timbre.
- Harmonics are distorted signals or wave forms. Harmonics as voltages or currents that at frequencies are a multiple of the fundamental frequency. In most systems, the fundamental frequency is 60 Hz. Therefore, harmonic order is 120 Hz, 180 Hz, 240 Hz and so on. (For European countries with 50 Hz systems, the harmonic order is 100 Hz, 150 Hz, 200 Hz, etc.) You can calculate a relationship between the fundamental and distorted waveforms by finding the square root of the sum of the squares of all harmonics generated by a single load, and then dividing this number by the nominal 60 Hz waveform value. You do this by a mathematical calculation known as a Fast Fourier Transform (FFT) theorem. (FFT is beyond the scope of this article. IEEE's Standard Dictionary of Electrical and Electronic Terms gives a definition of Fourier series.) This calculation method determines the total harmonic distortion (THD) contained within a nonlinear current or voltage waveform. Harmonics can cause overloading of conductors and transformers and overheating of utilization equipment, such as motors. Triplen harmonics can especially cause overheating of neutral conductors on 3-phase, 4-wire systems. While the fundamental frequency and even harmonics cancel out in the neutral conductor, odd-order harmonics are additive. Even in a balanced load condition, neutral currents can reach magnitudes as high as 1.73 times the average phase current. This additional loading creates more heat, which breaks down the insulation of the neutral conductor. In some cases, it can break down the insulation between winding of a transformer. In both cases, the result is a fire hazard. But, you can diminish this potential damage by using sound wiring practices. When most electrical engineers design the building's wiring, they usually leave the sizing of the neutral conductor to the dictates of NEC. In most cases, the installed neutral is the same size as the phase conductors.
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