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Harmonics 

    A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency (first harmonic) is 25 Hz, the frequencies of the next harmonics are: 50 Hz (2nd harmonic), 75 Hz (3rd harmonic), 100 Hz (4th harmonic) etc.

   Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at not one, but several frequencies known as partials. When the oscillator is long and thin, such as a guitar string, or the column of air in a trumpet, many of the partials are integer multiples of the fundamental frequency; these are called harmonics. Sounds made by long, thin oscillators are for the most part arranged harmonically, and these sounds are generally considered to be musically pleasing. Partials whose frequencies are not integer multiples of the fundamental are referred to as inharmonic partials. Instruments such as cymbals, pianos, and strings plucked pizzicato create inharmonic sounds.

Definition Provided by Wikipedia

Fundamental Frequency for one closed and one open end

 The fundamental frequency (or first harmonic) 

           length equals 1/4 Wavelength 



The second harmonic 

   length equals 3/4 wavelength 




The Third harmonic 

   length equal 1 1/4 wavelength 

  Fundamental Frequency for open ends

 The fundamental frequency (or first harmonic)

  length equals 1/2 Wavelength 



The second harmonic

length equals 1 wavelength 




The Third harmonic 

length equal 1 1/2 wavelength 

Fundamental frequency for closed end 

The fundamental frequency (or first harmonic)

length equals 1/2 Wavelength 




The second harmonic 

length equals 1 wavelength 



The Third harmonic 

length equal 1 1/2 wavelength