Biomedical Engineering Reference
In-Depth Information
The two arguments in the exponents represent waves traveling along the positive
z
-axis and
along the negative
-axis, respectively. For a constant frequency, for example, when the argu-
ment of the first term is equal to
z
, the term is real and has an amplitude of -1. The next time the
amplitude of the first term has this value is for an argument of 3
p
p
. For this situation, both
t
and
z
must increase; therefore, these arguments can be recognized as wavefronts that propagate
forward with a delay equal to the distance divided by the sound speed,
t
-
z
/
c
0
.
If
k
is a wavenumber defined as
k
¼
2
p
f
=
c
0
¼ o=
c
0
ð
16
:
8
Þ
and
is frequency, a sinusoidal wave can be interpreted as a function of propagation dis-
tance at a fixed time with a wavelength,
f
l ¼
2
p
/
k
, or as a function of time at a specific loca-
tion with a period,
, as shown in Figure 16.5.
The ratio of a traveling pressure wave,
T
¼
2
p
/
o
p
, to the particle velocity,
v
, of the fluid is called
the specific acoustic or characteristic impedance,
Z
L
¼
p
=
v
L
¼ r
c
L
ð
16
:
9
Þ
fixed time
z
λ
(a)
fixed z
t
T
(b)
FIGURE 16.5
(a) Sinusoidal acoustic wave propagation as a function of space at a fixed time. (b) Sinusoidal
acoustic wave propagation as a function of time at a fixed distance
; pressure is the acoustic parameter plotted
here. The distance and time between two troughs or peaks are defined as the wavelength, (l), and period, (
z
T
), of
the wave, respectively.
