Page 44 - The Master Handbook Of Acoustics

19
FUNDAMENTALS OF SOUND

concentrations of energy were located and measured with an elec-
tronic voltmeter.
For an ideal sine wave, all the energy is concentrated at one fre-
quency. The sine wave produced by this particular signal generator is not
really a pure sine wave. No oscillator is perfect and all have some har-
monic content, but in scanning the spectrum of this sine wave, the har-
monics measured were too low to show on the graph scale of Fig. 1-15.
The triangular wave of this signal generator has a major fundamental
component of 10 units magnitude. The wave analyzer detected a signif-
icant second harmonic component at f , twice the frequency of the fun-
2
damental with a magnitude of 0.21 units. The third harmonic showed
an amplitude of 1.13 units, the fourth of 0.13 units, etc. The seventh har-
monic still had an amplitude of 0.19 units and the fourteenth harmonic
(about 15 kHz in this case) an amplitude of only 0.03 units, but still eas-
ily detectable. So we see that this triangular wave has both odd and even
components of modest amplitude down through the audible spectrum.
If you know the amplitude and phases of each of these, the original tri-
angular wave shape can be synthesized by combining them.
A comparable analysis reveals the spectrum of the square wave
shown in Fig. 1-15. It has harmonics of far greater amplitude than the
triangular wave with a distinct tendency toward more prominent odd
than even harmonics. The third harmonic shows an amplitude 34 per-
cent of the fundamental! The fifteenth harmonic of the square wave is
still 0.52 units! If the synthesis of a square wave stops with the fif-
teenth harmonic, the wave of Fig. 1-16C results.
A glance at the spectra of sine, triangular, and square waves reveals
energy concentrated at harmonic frequencies, but nothing between.
These are all so-called periodic waves, which repeat themselves cycle
after cycle. The fourth example in Fig. 1-15 is a random noise. The
spectrum of this signal cannot be measured satisfactorily by a wave
analyzer with a 5-Hz passband because the fluctuations are so great
that it is impossible to get a decent reading on the electronic voltmeter.
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
until the drooping at high frequencies indicates that the upper fre-
quency limit of the random noise generator has been reached.