Even and Odd Harmonics of a vibrating string

Even and Odd Harmonics of a vibrating string

In the previous section we took a look at the vibrating string fixed at both ends and found that in order for the boundary condition to be satisfied, the following are the only solutions possible:†

Even and Odd harmonic animation

The solutions on the left of the image are often termed as ‘Odd Harmonics’ because they have odd number of anti-nodes and the ones of the right have even number of anti-nodes hence ‘Even Harmonics’


If you pluck a string right at the center, you are essentially exciting only the odd harmonic components.

Odd Harmonics of a Triangular wave

You can test this out by taking a string instrument and plucking it at the center. Download a spectrum app on your phone and take a look at the spectrum

Harmonics spectrum
Source video

You will see peaks in the spectrum only at the frequencies which correspond to the odd harmonics:

Odd harmonic spectrum

String instruments like the violin or guitar are plucked off-centered, so you get both the odd and even harmonics. But what differentiates one instrument from the other is the amplitude at which these harmonics are expressed when you play them.

Do watch the following video if you would like to know more:

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