124Audition
Soundintensity(I)isproportionaltopressure(p)squared:
I=p^2 poc,wherepoisthedensityofthemediuminwhich
soundtravels(e.g.,air).Soundintensityisapower(P)measure
oftherateatwhichworkcanbedoneandenergy(E)isthe
measureoftheamountofwork:I=P=ET,whereTistime.
The Decibel
In many situations involving sound, including hearing, the
range of measurable sound intensity is very large. The range
of sound intensity from the softest sound that one can detect
to the loudest sound one can tolerate (the dynamic range of
hearing) is on the order of 10^13. This large range led to the
decibel measure of sound intensity in which the decibel (dB)
is 10 times the logarithm of the ratio of two sound intensities:
dB= 10 log 10 (IIo),log 10 isthelogarithmtothebase10and
Ioisareferentsoundintensity.Becausesoundintensityispro-
portionaltopressuresquared,dB= 20 log 10 (ppo),wherepo
isareferentpressure.Thus,thedynamicrangeofhearingis
approximately130dB.
The decibel is a relative measure of sound intensity or
pressure. Several conventions have been adopted for the ref-
erent sound intensity (Io) or pressure (po). The most common
is the decibel measured in sound pressure level (SPL). In this
case,pois 20 micropascals (20 Pa). This is approximately
the sound pressure required for the average young adult to
just detect the presence of a tone (a sound produced by a si-
nusoidal vibration) whose frequency is in the region of 1000
to 4000 Hz. Thus, a measure such as 80 dB SPLmeans
thatthesoundpressurebeingmeasuredis80dBgreater(or
10,000timesgreater,20log 10 10,000=80dB)thanthe
thresholdofhearing(i.e.,80dBgreaterthan20 Pa).Most
often,decibelsareexpressedasdBSPL,butmanyother
conventionsarealsoused.
Reflections, Standing Waves, Reverberation,
and Sound Shadows
As a sound wave travels from its source toward the ears of a
listener, it will most likely encounter obstacles, including the
head and body of the listener. Sound can be absorbed in, re-
flected from, diffracted around, or transmitted to the medium
of the obstacle that the sound wave encountered. Each obsta-
cle offers an impedance to the transmission of the sound
wave to the medium of the obstacle. Impedance has three
main components. The medium can offer a resistance (R) to
the transmission of sound. The mass of the medium can offer
a mass reactance (Xm) that impedes the sound, and the
springlike inertia properties of the medium also produce
spring reactance (Xs). The impedance (Z) of the medium
equals[R^2 +(Xm–Xs)^2 ]. Thus, each obstacle has a char-
acteristic impedance, and the greater the difference in charac-
teristic impedance between two objects, the more sound is
reflected from and not transmitted to the new medium. The
characteristic impedance of an object is proportional to poc,
which is the denominator of the definition of sound intensity
(I=p^2 /poc). Thus, sound intensity is equal to pressure
squared divided by characteristic impedance.
When sound is reflected from an object, the reflected
sound wave can interact with the original sound wave, caus-
ing regions in which the two sound waves reinforce each
other or at other locations cancel each other. Under the proper
conditions, the reflected reinforcements and cancellations
can establish a standing wave. A standing wave represents
spatial locations in which the pressure is high (antinodes) due
to reinforcements and spatial locations where the pressure is
low nodes due to cancellations. The wavelength of a standing
wave (distance between adjacent nodes or antinodes) is de-
termined by the size of the environment in which the standing
wave exists. Large areas produce long standing-wave wave-
lengths and hence low frequencies, and the converse is true
for small areas. Thus, a standing wave in a short tube will
produce a high-frequency standing wave, and a long tube will
produce a low-frequency standing wave. This is the principal
upon which organ pipes and horns operate to produce musi-
cal notes. Structures in the auditory system, such as the outer
ear canal, can also produce standing waves.
The reflections from many surfaces can reinforce each
other and sustain sound in an environment long after the
sound has terminated. The time it takes this reverberation to
decline by 60 dB relative to the source level is the reverbera-
tion time of the environment. Rooms can support high speech
intelligibility and pleasant listening if there is some reverber-
ation, but not if the reverberation time is too long.
If the size of an object is large relative to a sound’s wave-
length, most of the sound will either be reflected from the ob-
ject or be transmitted to the object. Sound will be diffracted
around (bypass) an object whose size is much smaller than the
sound’s wavelength. When the wavelength of sound is ap-
proximately the same as the size of an object, some of the
sound is reflected from the object and some is diffracted
around the object. The result is that there is an area on the side
of the object opposite from where the sound originated where
the sound pressure is lower. Thus, such an object produces a
sound shadow in an area very near the object, where there is a
lower sound pressure than there is in areas farther away from
the object. The head, for instance, produces a sound shadow
at the far ear when the frequency of sound arriving at the lead
ear is generated by a sound with a wavelength that is approx-
imately equal to or smaller than the size of the head.