Page 42 - Master Handbook of Acoustics

FIGURE 1-14 A square wave can be synthesizing by adding harmonics to the sine-wave

fundamental. (A) A square wave (with an infinite number of harmonic components). (B) The
summation of the fundamental and two nonzero harmonic components. (C) The summation of the
fundamental and nine nonzero harmonic components. Clearly, many components would be needed to
smooth the ripples and produce the square corners of (A).

The spectra of sine, triangular, and square waves reveal energy concentrated at harmonic
frequencies, but nothing between. These are all periodic waveforms, which repeat themselves cycle
after cycle. The fourth example in Fig. 1-13D is random (white) noise. The spectrum of this signal
cannot be measured satisfactorily by a waveform analyzer with a 5-Hz passband because the

fluctuations are so great that it is impossible to get an accurate reading. Analyzed by a wider
passband of fixed bandwidth and with the help of various integrating devices to get a steady
indication, the spectral shape shown is obtained. This spectrum tells us that the energy of the random-
noise signal is equally distributed throughout the spectrum; the roll-off at high frequencies indicates
that the upper frequency limit of the random-noise generator has been reached.

There is little visual similarity between the sine and the random-noise signals as revealed by an
oscilloscope, yet there is a hidden relationship. Even random noise can be considered as comprising
sine-wave components constantly shifting in frequency, amplitude, and phase. If we pass random
noise through a narrow filter and observe the filter output on an oscilloscope, we will see a restless,
sinelike wave continually shifting in amplitude. Theoretically, an infinitely narrow filter would sift
out a pure sine wave.

Electrical, Mechanical, and Acoustical Analogs

An acoustical system such as a loudspeaker can be represented in terms of an equivalent electrical or
mechanical system. An engineer uses these equivalents to set up a mathematical approach for

analyzing a given system. For example, the effect of a cabinet on the functioning of a loudspeaker is
clarified by thinking of the air in the enclosed space as acting like a capacitor in an electric circuit,
absorbing and giving up the energy imparted by the cone movement.
Figure 1-15 shows the graphical representation of the three basic elements in electrical,
mechanical, and acoustical systems. Inductance in an electric circuit is equivalent to mass in a
mechanical system and inertance in an acoustical system. Capacitance in an electric circuit is

analogous to compliance in a mechanical system and capacitance in an acoustical system. Resistance
is resistance in all three systems, whether it is the frictional losses offered to air-particle movement
in glass fiber, frictional losses in a wheel bearing, or resistance to the flow of current in an electric
circuit.