Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
Figure 2.11 Harmonic frequencies
Like a rope held at both ends, a guitar string fixed at both ends creates a standing wave as
it vibrates according to its resonant frequencies. In a standing wave, there exist points in the
wave that don‟t move. These are called the nodes, as pictured in Figure 2.11. The antinodes are
the high and low points between which the string vibrates. This is hard to illustrate in a still
image, but you should imagine the wave as if it‟s anchored at the nodes and swinging back and
forth between the nodes with high and low points at the antinodes.
It‟s important to note that this figure illustrates the physical movement of the string, not a
graph of a sine wave representing the string‟s sound. The string‟s vibration is in the form of a
transverse wave, where the string moves up and down while the tensile energy of the string
propagates perpendicular to the vibration. Sound is a longitudinal wave.
The speed of the wave‟s propagation through the string is a function of the tension force
on the string, the mass of the string, and the string‟s length. If you have two strings of the same
length and mass and one is stretched more tightly than another, it will have a higher wave
propagation speed and thus a higher frequency. The frequency arises from the properties of the
string, including its fundamental wavelength, 2L, and the extent to which it is stretched.
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