A dipole source can vibrate in any axis and thereby differs from the symmetrical, radial motion of a pulsating sphere, where the magnitude of
motion is equal in all directions. The direction of particle displacement in
the near field close to the source follows a path from the front of the sphere
(defined by the initial direction of displacement) back to its rear (Fig.
2.3B(a)).
Kalmijn (1988) recognizes an additional near-field region of “intermediate flow” for a dipole source whose fluid velocities are like those of the rest
of the near field. Also, unlike the monopole source, the amplitude of particle motion in the dipole’s far field is asymmetrical and increases from
a minimum along an axis perpendicular to the direction of motion to a
maximum along the axis of motion (Fig. 2.3B(b)).
Net fluid displacement, velocity, and acceleration attenuate at the rate of
1/r
3 in the dipole’s near-field region dominated by hydrodynamic flow and
as 1/r
2 in the intermediate flow region. Unlike the monopole source, the
local flow pressure falls off at the rate of 1/r
2 in the near field. However,
like a monopole, the propagating sound wave’s displacement, velocity,
acceleration, and pressure all attenuate at a rate that is proportional to 1/r
with increasing source distance.
The reader is encouraged to consult Kalmijn’s (1988) essay for a complete explanation of the physical principles, namely the inertial and compressional forces, that establish the local flow field and the propagating
sound wave. In Section 4.1, we will focus on the loss of acoustic energy for
the propagating sound wave mainly because it is the component of the
sound field commonly measured for the characterization of acoustic communication signals in water and air. The reader is also encouraged to refer
to reviews by Coombs and Janssen (1988) and Kalmijn (1989) for a consideration of dipoles in regard to the operation of the mechanosensory
lateral-line system.
3.3. Wavelength Dependency of Near- and
Far-Field Range
Because the amplitude of particle motion in the local flow region of
the near and intermediate fields decreases much faster than that of the
propagating sound wave (see above), the latter comes to dominate the
spread of acoustic energy as distance from the source increases for either
a monopole or a dipole source. The change in strength of the local flow
and propagating sound wave with increasing source distance is wavelengthdependent (see Fig. 2 in Coombs and Janssen 1988). For a monopole source,
the theoretical prediction for the point at which the local flow and the
propagating sound wave contribute equally to the sound wave is at a
distance of about l/2p from the source; the propagating wave dominates
beyond that point. For a dipole source, the local flow region of the near
field predominates up to a distance of about l/2p from the source, whereas
24
A.H. Bass and C.W. Clark
motion is equal in all directions. The direction of particle displacement in
the near field close to the source follows a path from the front of the sphere
(defined by the initial direction of displacement) back to its rear (Fig.
2.3B(a)).
Kalmijn (1988) recognizes an additional near-field region of “intermediate flow” for a dipole source whose fluid velocities are like those of the rest
of the near field. Also, unlike the monopole source, the amplitude of particle motion in the dipole’s far field is asymmetrical and increases from
a minimum along an axis perpendicular to the direction of motion to a
maximum along the axis of motion (Fig. 2.3B(b)).
Net fluid displacement, velocity, and acceleration attenuate at the rate of
1/r
3 in the dipole’s near-field region dominated by hydrodynamic flow and
as 1/r
2 in the intermediate flow region. Unlike the monopole source, the
local flow pressure falls off at the rate of 1/r
2 in the near field. However,
like a monopole, the propagating sound wave’s displacement, velocity,
acceleration, and pressure all attenuate at a rate that is proportional to 1/r
with increasing source distance.
The reader is encouraged to consult Kalmijn’s (1988) essay for a complete explanation of the physical principles, namely the inertial and compressional forces, that establish the local flow field and the propagating
sound wave. In Section 4.1, we will focus on the loss of acoustic energy for
the propagating sound wave mainly because it is the component of the
sound field commonly measured for the characterization of acoustic communication signals in water and air. The reader is also encouraged to refer
to reviews by Coombs and Janssen (1988) and Kalmijn (1989) for a consideration of dipoles in regard to the operation of the mechanosensory
lateral-line system.
3.3. Wavelength Dependency of Near- and
Far-Field Range
Because the amplitude of particle motion in the local flow region of
the near and intermediate fields decreases much faster than that of the
propagating sound wave (see above), the latter comes to dominate the
spread of acoustic energy as distance from the source increases for either
a monopole or a dipole source. The change in strength of the local flow
and propagating sound wave with increasing source distance is wavelengthdependent (see Fig. 2 in Coombs and Janssen 1988). For a monopole source,
the theoretical prediction for the point at which the local flow and the
propagating sound wave contribute equally to the sound wave is at a
distance of about l/2p from the source; the propagating wave dominates
beyond that point. For a dipole source, the local flow region of the near
field predominates up to a distance of about l/2p from the source, whereas
24
A.H. Bass and C.W. Clark