Fundamental Frequency and Harmonics

Each natural frequency that an object or instrument produces has its own characteristic vibrational mode or standing wave pattern. These patterns are only created within the object or instrument at specific frequencies of vibration; these frequencies are known as harmonic frequencies, or merely harmonics. At any frequency other than a harmonic frequency, the resulting disturbance of the medium is irregular and non-repeating. For musical instruments and other objects that vibrate in regular and periodic fashion, the harmonic frequencies are related to each other by simple whole number ratios. This is part of the reason why such instruments sound pleasant

First, consider a guitar string vibrating at its natural frequency or harmonic frequency. Because the ends of the string are attached and fixed in place to the guitar’s structure (the bridge at one end and the frets at the other), the ends of the string are unable to move. Subsequently, these ends become nodes – points of no displacement. In between these two nodes at the end of the string, there must be at least one antinode. The most fundamental harmonic for a guitar string is the harmonic associated with a standing wave having only one antinode positioned between the two nodes on the end of the string. This would be the harmonic with the longest wavelength and the lowest frequency. The lowest frequency produced by any particular instrument is known as the fundamental frequency. The fundamental frequency is also called the first harmonic of the instrument.

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http://www.physicsclassroom.com/Class/sound/u11l4d.cfm

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