34 Chapter 2
An impedance phase plot often accompanies an
impedance magnitude plot to show whether the loud-
speaker load is resistive, capacitive, or inductive at a
given frequency. A resistive load will convert the
applied power into heat. A reactive load will store and
reflect the applied power. Complex loads, such as loud-
speakers, do both. When considering the power deliv-
ered to the loudspeaker, the impedance Z is used in the
power equation. When considering the power dissipated
by the load, the resistive portion of the impedance must
be used in the power equation. The power factor
describes the reduction in power transfer caused by the
phase angle between voltage and current in a reactive
load. Some definitions are useful.
(2-16)(2-17)(2-18)where,
T is the phase angle between the voltage and current.
Ohm’s Law and the power equation in its various
forms are foundation stones of the audio field. One can
use these important tools for a lifetime and not exhaust
their application to the electrical and acoustical aspects
of the sound reinforcement system.
2.9 Human Hearing
It is beneficial for sound practitioners to have a basic
understanding of the way that people hear and perceive
sound. The human auditory system is an amazing
device, and it is quite complex. Its job is to transduce
fluctuations in the ambient atmospheric pressure into
electrical signals that will be processed by the brain and
perceived as sound by the listener. We will look at a few
characteristics of the human auditory system that are of
significance to audio practitioners.
The dynamic range of a system describes the differ-
ence between the highest level that can pass through the
system and its noise floor. The threshold of human
hearing is about 0.00002 Pascals (Pa) at mid frequen-
cies. The human auditory system can withstand peaks of
up to 200 Pa at these same frequencies. This makes the
dynamic range of the human auditory system
approximately
(2-19)The hearing system can not take much exposure at
this level before damage occurs. Speech systems are
often designed for 80 dB ref. 20μPa and music systems
about 90 dB ref. 20μPa for the mid-range part of the
spectrum.
Audio practitioners give much attention to achieving
a flat spectral response. The human auditory system is
not flat and its response varies with level. At low levels,
its sensitivity to low frequencies is much less than its
sensitivity to mid-frequencies. As level increases, the
difference between low- and mid-frequency sensitivity
is less, producing a more uniform spectral response. The
classic equal loudness contours, Fig. 2-17, describe this
phenomenon and have given us the weighting curves,
Fig. 2-18, used to measure sound levels.
Modern sound systems are capable of producing
very high sound pressure levels over large distances.
Great care must be taken to avoid damaging the hearing
of the audience.
The time response of the hearing system is slow
compared to the number of audible events that can
occur in a given time span. As such, our hearing system
integrates closely spaced sound arrivals (within about
35 ms) with regard to level. This is what makes sound
indoors appear louder than sound outdoors. While
reflected sound increases the perceived level of a sound
source, it also adds colorations. This is the heart of how
we perceive acoustic instruments and auditoriums. A
good recording studio or concert hall produces a musi-
cally pleasing reflected sound field to a listener posi-
tion. In general, secondary energy arrivals pose
problems if they arrive earlier than 10 ms (severe tonal
coloration) after the first arrival or later than 50 ms
(potential echo), Fig. 2-19.
The integration properties of the hearing system
make it less sensitive to impulsive sound events with
regard to level. Peaks in audio program material are
often 20 dB or more higher in level than the perceived
loudness of the signal. Program material that measures
90 dBA (slow response) may contain short term events
at 110 dBA or more, so care must be taken when
exposing musicians and audiences to high powered
sound systems.
The eardrum is a pressure sensitive diaphragm that
responds to fluctuations in the ambient atmospheric
pressure. Like a loudspeaker and microphone, it has an
overload point at which it distorts and can be damaged.Apparent Power Total Power E2Z----- -=Active Power Absorbed Power E2
R----- -=Reactive Power Reflected Power E2ZcosT=---------------DR 20 200
0.00002= log-------------------=140 dB