5
2
Fundamentals of
Acoustic Propagation
Ultrasound is a sound wave characterized by such parameters as pressure, particle (or
medium) velocity, particle displacement, density, and temperature. It differs from a
sound wave in that its frequency is higher than 20
×
10
3
cycles per second or 20 kHz
(kilohertz). The audible range of human ear is from 20 Hz to 20 kHz. Because
ultrasound is a wave, it transmits energy just like an electromagnetic wave or radiation.
Unlike an electromagnetic wave, however, sound requires a medium in which to travel
and thus cannot propagate in a vacuum.
To better visualize how the sound propagates through a homogeneous medium,
the medium can be modeled as a three-dimensional matrix of elements, which may
represent molecules, atoms, or elemental particles, separated by perfect elastic
springs representing interelement forces. To simplify the matter even more, only a
two-dimensional lattice is shown in Figure 2.1, in which the elements are repre-
sented by spheres. When a particle is pushed to a distance from its neutral position,
the disturbance or force is transmitted to the adjacent particle by the spring. This
creates a chain reaction. If the driving force is oscillating back and forth or sinu-
soidally, the particles respond by oscillating in the same way. The distance,
U
,
traveled by the particle in the acoustic propagation is called particle or medium
displacement, usually in the order of a few tenths of a nanometer in water. The
velocity of the particle oscillating back and forth is called particle or medium
velocity,
u
, and is in the order of a few centimeters per second in water. It must be
noted that this velocity is different from the rate at which the energy is propagating
through the medium.
The velocity at which the ultrasound energy propagates through the medium
is defined as the phase velocity or the sound propagation velocity,
c
. In water,
c
=
1500 m/s. This is illustrated in Figure 2.1, which shows that the sound velocity is
much faster than the particle velocity. Although the particle has only moved a short
distance, the perturbation has already been transmitted to other particles over a
much longer distance,
U
′
. As a sinusoidal disturbance is propagated into a liquid
medium, regions of medium compression and rarefaction will be produced, as
shown in Figure 2.2. The displacement of the particles,
U
, is in the same direction
as the direction of wave propagation,
X
. This type of wave is called a longitudinal
or compressional wave.
The particle displacement in the rarefaction region is the largest and it is the
smallest in the compression. If the displacement of the particles vs. distance or the
displacement of a particle vs. time is plotted, it can be seen that the particle moves
in a sinusoidal format as shown in Figure 2.3. The wavelength of a sound wave,
λ
,
is defined as the distance between two points of the same phase in space. For example,
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