Page 45 - The Master Handbook Of Acoustics

20 CHAPTER ONE

There is little visual similarity between
the sine and the random-noise signals as
revealed by the cathode-ray oscilloscope,
A
yet there is a hidden relationship. Even ran-
dom noise can be considered as being made
up of sine-wave components constantly
shifting in frequency, amplitude, and
phase. If you pass random noise through a
B
narrow filter and observe the filter output
on a cathode-ray oscilloscope, you will see
a restless, sinelike wave that constantly
shifts in amplitude. Theoretically, an infi-
nitely narrow filter would sift out a pure,
C
but nervous, sine wave. (See chapter 5.)

Electrical, Mechanical, and
FIGURE 1-16
Acoustical Analogs
In synthesizing the square wave of (A), including
only the fundamental and two harmonics yields (B). An acoustical system such as a loud-
Including fifteen components yields (C). It would speaker can be represented in terms of an
take many more than fifteen harmonics to smooth
the ripples and produce the square corners of (A). equivalent electrical or mechanical sys-
tem. The physicist freely uses these equiv-
alents to set up his mathematical approach
for analyzing a given system. Although such approaches are far out-
side the scope of this book, it is useful to develop some appreciation
for these methods. For example, the effect of a cabinet on the func-
tioning of a loudspeaker is clarified by thinking of the air in the
enclosed space as acting like a capacitor in an electrical circuit,
absorbing and giving up the energy imparted by the cone movement.
Figure 1-17 shows the graphical representation of the three basic
elements in electrical, mechanical, and acoustical systems. Inductance
in an electrical circuit is equivalent to mass in a mechanical system
and inertance in an acoustical system. Capacitance in an electrical cir-
cuit is analogous to compliance in a mechanical system and capaci-
tance in an acoustical system. Resistance is resistance in all three
systems, whether it be the frictional losses offered to air-particle move-
ment in glass fiber, frictional losses in a wheel bearing, or resistance to
the flow of current in an electrical circuit.