Fundamentals of Audio and Acoustics 232.1 Introduction
Many people get involved in the audio trade prior to
experiencing technical training. Those serious about
practicing audio dig in to the books later to learn the
physical principles underlying their craft. This chapter is
devoted to establishing a baseline of information that will
prove invaluable to anyone working in the audio field.
Numerous tools exist for those who work on sound
systems. The most important are the mathematical tools.
Their application is independent of the type of system
or its use, plus, they are timeless and not subject to
obsolescence like audio products. Of course, one must
always balance the mathematical approach with
real-world experience to gain an understanding of the
shortcomings and limitations of the formulas. Once the
basics have been mastered, sound system work becomes
largely intuitive.
Audio practitioners must have a general under-
standing of many subjects. The information in this
chapter has been carefully selected to give the reader the
big picture of what is important in sound systems. Many
of the topics are covered in greater detail in other chap-
ters of this book. In this initial treatment of each subject,
the language of mathematics has been kept to a
minimum, opting instead for word explanations of the
theories and concepts. This provides a solid foundation
for further study of any of the subjects. Considering the
almost endless number of topics that could be included
here, I selected the following based on my own experi-
ence as a sound practitioner and instructor. They are:
- The Decibel and Levels.
- Frequency and Wavelength.
- The Principle of Superposition.
- Ohm’s Law and the Power Equation.
- Impedance, Resistance, and Reactance.
- Introduction to Human Hearing.
- Monitoring Audio Program Material.
- Sound Radiation Principles.
- Wave Interference.
A basic understanding in these areas will provide the
foundation for further study in areas that are of partic-
ular interest to the reader. Most of the ideas and princi-
ples in this chapter have existed for many years. While I
haven’t quoted any of the references verbatim, they get
full credit for the bulk of the information presented here.
2.2 The Decibel
Perhaps the most useful tool ever created for audio prac-
titioners is the decibel (dB). It allows changes in system
parameters such as power, voltage, or distance to be
related to level changes heard by a listener. In short, the
decibel is a way to express “how much” in a way that is
relevant to the human perception of loudness. We will
not track its long evolution or specific origins here. Like
most audio tools, it has been modified many times to
stay current with the technological practices of the day.
Excellent resources are available for that information.
What follows is a short study on how to use the decibel
for general audio work.
Most of us tend to consider physical variables in
linear terms. For instance, twice as much of a quantity
produces twice the end result. Twice as much sand
produces twice as much concrete. Twice as much flour
produces twice as much bread. This linear relationship
does not hold true for the human sense of hearing.
Using that logic, twice the amplifier power should
sound twice as loud. Unfortunately, this is not true.
Perceived changes in the loudness and frequency of
sound are based on the percentage change from some
initial condition. This means that audio people are
concerned with ratios. A given ratio always produces
the same result. Subjective testing has shown that the
power applied to a loudspeaker must be increased by
about 26% to produce an audible change. Thus a ratio of
1.26:1 produces the minimum audible change, regard-
less of the initial power quantity. If the initial amount of
power is 1 watt, then an increase to 1.26 watts (W) will
produce a “just audible” increase. If the initial quantity
is 100 W, then 126 W will be required to produce a just
audible increase. A number scale can be linear with
values like 1, 2, 3, 4, 5, etc. A number scale can be
proportional with values like 1, 10, 100, 1000, etc. A
scale that is calibrated proportionally is called a loga-
rithmic scale. In fact, logarithm means “proportional
numbers.” For simplicity, base 10 logarithms are used
for audio work. Using amplifier power as an example,
changes in level are determined by finding the ratio of
change in the parameter of interest (e.g. wattage) and
taking the base 10 logarithm. The resultant number is
the level change between the two wattages expressed in
Bels. The base 10 logarithm is determined using a
look-up table or scientific calculator. The log conver-
sion accomplishes two things:- It puts the ratio on a proportional number scale that
better correlates with human hearing. - It allows very large numbers to be expressed in a
more compact form, Fig. 2-1.
The final step in the decibel conversion is to scale
the Bel quantity by a factor of ten. This step converts
Bels to decibels and completes the conversion process,