Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013

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frequencies, all of which give an instrument its characteristic sound. The

fundamental and harmonic frequencies are also referred to as the partials, since

together they make up the full sound of the resonating object. The harmonic

frequencies beyond the fundamental are called overtones. These terms can be

slightly confusing. The fundamental frequency is the first harmonic because

this frequency is one times itself. The frequency that is twice the fundamental is

called the second harmonic or, equivalently, the first overtone. The frequency

that is three times the fundamental is called the third harmonic or second

overtone, and so forth. The number of harmonic frequencies depends upon the

properties of the vibrating object.

One simple way to understand the sense in which a frequency might be natural to an

object is to picture pushing a child on a swing. If you push a swing when it is at the top of its

arc, you‟re pushing it at its resonant frequency, and you‟ll get the best effect with your push.

Imagine trying to push the swing at any other point in the arc. You would simply be fighting

against the natural flow. Another way to illustrate resonance is by means of a simple transverse

wave, as we‟ll show in the next section.

2.1.4.2 Resonance of a Transverse Wave

We can observe resonance in the example of a simple transverse wave that

results from sending an impulse along a rope that is fixed at both ends. Imagine

that you‟re jerking the rope upward to create an impulse. The widest upward

bump you could create in the rope would be the entire length of the rope. Since

a wave consists of an upward movement followed by a downward movement,

this impulse would represent half the total wavelength of the wave you‟re

transmitting. The full wavelength, twice the length of the rope, is conceptualized

in Figure 2.9. This is the fundamental wavelength of the fixed-end transverse

wave. The fundamental wavelength (along with the speed at which the wave is

propagated down the rope) defines the fundamental frequency at which the

shaken rope resonates.

If

L

is the length of a rope fixed at both ends, then

is the fundamental wavelength of the

rope, given by

2L

Equation 2.4

Figure 2.9 Full wavelength of impulse sent through fixed-end rope

Now imagine that you and a friend are holding a rope between you and shaking it up and

down. It‟s possible to get the rope into a state of vibration where there are stationary points and

other points between them where the rope vibrates up and down, as shown in Figure 2.10. This

Video

Tutorial:

String

Resonance

Flash

Tutorial:

Resonance as

Harmonic

Frequencies