Page 59 - Master Handbook of Acoustics

FIGURE 2-4 Amplitude relationships for sinusoids apply to sine waves of electrical voltage or

current, as well as to acoustical parameters such as sound pressure. Another term used in the audio
field is crest factor, or peak divided by RMS. These mathematical relationships apply to sine waves
and cannot be applied to complex waveforms.

The common ac (alternating current) voltmeter is, in reality, a dc (direct current) instrument fitted
with a rectifier that changes the alternating sine-wave current to pulsating unidirectional current. The
dc meter then responds to the average value, as indicated in Fig. 2-4. However, such meters are
almost universally calibrated in terms of RMS (root-mean-square, described as follows). For pure
sine waves, this is quite an acceptable fiction, but for nonsinusoidal waveforms, the reading will be

in error.
An alternating current of 1 A (ampere) RMS (or effective) is exactly equivalent in heating power
to 1 A of direct current as it flows through a resistance of known value. After all, alternating current
can heat a resistor or do work no matter which direction it flows; it is just a matter of evaluating it. In
the right-hand positive curve of Fig. 2-4, the ordinates (height of lines to the curve) are read for each

marked increment of time. Then (a) each of these ordinate values is squared, (b) the squared values
are added together, (c) the average is found, and (d) the square root is taken of the average (or mean).
Taking the square root of this average gives the RMS (root-mean-square) value of the positive curve
of Fig. 2-4. The same can be done for the negative curve (squaring a negative ordinate gives a
positive value), but simply doubling the positive curve of a symmetrical waveform is easier. In this
way, the RMS or “heating-power” value of any alternating or periodic waves can be determined,
whether the wave represents voltage, current, or sound pressure. Figure 2-4 also provides a summary

of relationships pertaining only to the sine wave. It is important to remember that simple mathematical
relationships properly describe sine waves, but they cannot be applied to complex sounds.