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The fundamental frequency or original wave is known as the first harmonic. The following harmonics are referred to as higher harmonics. The fundamental frequency of every harmonic is periodic and the total number of harmonics is also periodic at that particular frequency.
The fundamental frequency of a vibrating body is its lowest resonant frequency. Most vibrating bodies have several resonant frequencies, and those employed in musical instruments often resonate at harmonics of the fundamental frequency.
An integer (whole number) multiple of the fundamental frequency is defined as a harmonic. Vibrating membranes normally create vibrations at harmonic frequencies, but they also contain certain non-harmonic resonant frequencies.
Frequency
Frequency is the rate of occurrence of vibration. It is measured in Hertz (Hz), which is evaluated by determining the number of oscillations (vibrations) per second. For example, a frequency which oscillates 100 times per second is expressed as a frequency of 100 Hz. When pitch is produced, it creates a sound wave that oscillates at a specific frequency, the fundamental/basic frequency, but also causes other higher frequencies to vibrate. These vibrations are called composite frequencies as they are the result of vibrations of fundamental frequency.
When the fundamental frequency and its composite frequencies are recognized by a listener then they are hardly heard as separate pitches. A listener is likely to perceive all the frequencies wrapped together so that it forms what we called as composite tone. When an instrument produces a pitch, it will inherently generate a range of composite frequencies which add to the richness of the tone that allow us to differentiate the qualities of sound, like the difference between the sound of a violin, and the sound of a guitar.
Overtones
An overtone is defined as a composite frequency which vibrates at a higher frequency than the fundamental frequency, whether it is a harmonic or not. Mostly every overtones of an instrument are also harmonic, and for this reason the two terms are often used interchangeably. However, there are some instruments which produce overtones that are not harmonic, particularly percussion instruments.
Source of Harmonics
Harmonics occur due to non-linear loads like iron-core inductors, rectifiers, switching transformers, electronic ballasts in fluorescent light, discharge lamps, saturated magnetic devices, and other high-inductance loads.
Effect of Harmonics
- Harmonic frequencies in the power grid were caused due to power quality problems.
- Harmonics in the power system result in increased heating of equipment and conductors and develop a pulsating torque in motors.
- Harmonics cause increasing operating temperature and the iron losses in AC motors and also in transformers as the hysteresis loss is directly proportional to the frequency and eddy current loss is directly proportional to square of frequency.
Modes of Harmonics
- First Harmonic: Fundamental frequency of an instrument is known as the First Harmonic of that instrument.
- Second Harmonic: The second harmonic of an instrument is produced by adding one more node between the ends of that instrument.
- Third Harmonic: The third harmonic of an instrument is produced by adding two more nodes between the ends of that instrument.
For a signal with fundamental frequency is f the harmonic mode is
The frequency of second harmonic is 2f.
The frequency of third harmonic is 3f,
The frequency of fourth harmonic is 4f, and so on.
Let w is the wavelength of the signal in a given medium then
The wavelength of second harmonic is w/2
The wavelength of third harmonic is w/3
The wavelength of fourth harmonic is w/4
Signals obtained at frequencies 2f, 4f, 6f, 8f, …. are even harmonics. And signals at frequencies 3f, 5f and 7f are odd harmonics. A signal can (theoretically) contains infinite number of harmonics.
Harmonic Distortion
In electrical distribution systems, harmonic distortion is the variation of standard voltage and current which results from the changes in frequency.
Harmonic Motion
In physics, harmonic motion, or simple harmonic motion, illustrate repetitive back and forth motion through a central or positional equilibrium. In this case, the maximum displacement on one side is equal to the total displacement on the other(opposite) side.
The interval of each complete oscillation is always same. The force which creates the motion is always directed toward the centre or equilibrium position. It is always proportional to the distance from it.
Time Harmonic
The harmonics produced by a source which changes non-sinusoidal in time and always present in the input supply are termed as time harmonics.
Space Harmonic
The harmonics produced by non-sinusoidal distribution of coils in the machine and due to which the air gap and flux are not sinusoidally distributed in space are termed as space harmonics.
Conclusion
Harmonics is defined as a signal or wave whose frequency is the integral (whole number) multiple of the frequency having same reference wave. As it is a part of the harmonic series, it can also refer to the ratio of the frequency of a signal or wave to the frequency of the reference signal (or wave).
For a signal with fundamental frequency is f the harmonic mode is
The frequency of Second harmonic is 2f.
The frequency of third harmonic is 3f.
The frequency of fourth harmonic is 4f, and so on.
Harmonics occur due to non-linear loads like iron-core inductors, rectifiers, switching transformers, electronic ballasts in fluorescent light, discharge lamps, saturated magnetic devices, and other high-inductance loads.
