Page 29 - The Master Handbook Of Acoustics

4 CHAPTER ONE

Amplitude relationships
for
sinusoids

Amplitude RMS Average Peak Peak

to
Time peak

Peak
RMS (0.707) (Peak)
√2

(Average) (1.1) (Average)
2√2
Peak (√2 ) (RMS) ( 1.414) (RMS)

2 (1.57) (Average)
( ) (Average)
FIGURE 1-3
Amplitude relationships for sinusoids, which apply to sine waves of electrical voltage or
current, as well as to acoustical parameters such as sound pressure. Another term which
is widely used in the audio field is crest factor, or peak divided by rms.

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 root-mean-square or rms value of the positive
loop of Fig. 1-3. The same can be done for the negative loop (squaring a
negative ordinate gives a positive value), but simply doubling the pos-
itive loop of a symmetrical wave is easier. In this way the root-mean-
square or “heating power” value of any alternating or periodic waves
can be determined whether the wave is for voltage, current, or sound
pressure. Such computations will help you understand the meaning of
rms, but fortunately reading meters is far easier. Figure 1-3 is a useful
summary of relationships pertaining only to the sine wave.