Fundamentals of Psychoacoustics
165
RMS
threshold of hearing
threshold of pain
intensity level
decibel
sound pressure level
transversal velocity
base <- position along the basilar membrane -> apex
velocity
Figure 2: Cartoon of the transversal velocity pattern elicited by an incoming
pure sine tone
is carried by a wave front. It is a vectorial quantity having magnitude
I =
p
2
max
2
1
z
0
=
p
2
max
2c
=
p
2
RM S
c
,
(4)
where p
max
and p
RM S
are the peak and root-mean-square (RMS) values of
pressure wave, respectively, and z
0
= c = density × speed is the impedance of
air.
At 1000Hz the human ear can detect sound intensities ranging from I
min
=
10
-12
W/m
2
(threshold of hearing) to I
max
= 1W/m
2
(threshold of pain).
Consider two spherical shells of areas a
1
and a
2
, at distances r
1
and r
2
from the point source. The lossless propagation of a wavefront implies that the
intensities registered at the two distances are related to the areas by
I
1
a
1
= I
2
a
2
.
(5)
Since the area is proportional to the square of distance from the source, we also
have
I
1
I
2
=
r
2
r
1
2
.
(6)
The intensity level is defined as
IL = 10 log
10
I
I
0
,
(7)
where I
0
= 10
-12
W/m
2
is the sound intensity at the threshold of hearing. The
intensity level is measured in decibel (dB), so that multiplications by a factor
are turned into additions by an offset, as represented in table C.2. Similarly, the
sound pressure level is defined as
SP L = 20 log
10
p
max
p
0,max
= 20 log
10
p
RM S
p
0,RM S
(8)