Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
multiples of the fundamental. All the resonant frequencies of an instrument can be present
simultaneously. They make up the frequency components of the sound emitted by the
instrument. The components may be excited at a lower energy and fade out at different rates,
however. Other frequencies contribute to the sound of an instrument as well, like the squeak of
fingers moving across frets, the sound of a bow pulled across a string, or the frequencies
produced by the resonant chamber of a guitar‟s body. Instruments are also characterized by the
way their amplitude changes over time when they are plucked, bowed, or blown into. The
changes of amplitude are called the amplitude envelope, as we‟ll discuss in a later section.
Resonance is one of the phenomena that gives musical instruments their characteristic
sounds. Guitar strings alone do not make a very audible sound when plucked. However, when a
guitar string is attached to a large wooden box with a shape and size that is proportional to the
wavelengths of the frequencies generated by the string, the box resonates with the sound of the
string in a way that makes it audible to a listener several feet away. Drumheads likewise do not
make a very audible sound when hit with a stick. Attach the drumhead to a large box with a size
and shape proportional to the diameter of the membrane, however, and the box resonates with
the sound of that drumhead so it can be heard. Even wind instruments benefit from resonance.
The wooden reed of a clarinet vibrating against a mouthpiece makes a fairly steady and quiet
sound, but when that mouthpiece is attached to a tube, a frequency will resonate with a
wavelength proportional to the length of the tube. Punching some holes in the tube that can be
left open or covered in various combinations effectively changes the length of the tube and
allows other frequencies to resonate.
2.1.5 Digitizing Sound Waves
In this chapter, we have been describing sound as continuous changes of air pressure amplitude.
In this sense, sound is an analog phenomenon a physical phenomenon that could be
represented as continuously changing voltages. Computers require that we use a discrete
representation of sound. In particular, when sound is captured as data in a computer, it is
represented as a list of numbers. Capturing sound in a form that can be handled by a computer is
a process called analog-to-digital conversion, whereby the amplitude of a sound wave is
measured at evenly-spaced intervals in time typically 44,100 times per second, or even more.
Details of analog-to-digital conversion are covered in Chapter 5. For now, it suffices to think of
digitized sound as a list of numbers. Once a computer has captured sound as a list of numbers, a
whole host of mathematical operations can be performed on the sound to change its loudness,
pitch, frequency balance, and so forth. We'll begin to see how this works in the following
2.2 Applications
2.2.1 Acoustics
In each chapter, we begin with basic concepts in Section 1 and give applications of those
concepts in Section 2. One main area where you can apply your understanding of sound waves
is in the area of acoustics. "Acoustics" is a large topic, and thus we have devoted a whole
chapter to it. Please refer to Chapter 4 for more on this topic.
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