150
15–20 m). In a tank experiment on midshipman directionalization (Coffin et al. 2014)
intended to approximate that environment, it was observed that females were generally able to resolve the 180° ambiguity and localize the sound source. Acoustic field
measurements in the tank and a method-of-images propagation model for the natural environment indicated that the time average intensity pointed in the wrong direction (i.e., towards the source) from a distance of 1 cm from the source out to a
distance beyond the release point, a meter from the source. This conclusion however
is called into question because the propagation model that was used has been determined to be invalid for a source and receiver so close to the bottom in such shallow
water. The field measurements in the Bodega Bay tank also indicated reversal of the
direction of the time averaged intensity vector but an erroneous phase in such measurements is always a possibility. Thus the question of whether the sign of the timeaveraged intensity could point in the wrong direction due to boundary conditions
direction remains moot. It is evident from the result shown for the point cardioid
that the sign of the time-averaged intensity can change as the field point moves
along the main response axis. Note that the intensity vector for a cardioid source
points to the left on both sides of the source in the near field (Fig. 10c) implying that
a fish approaching the source along the axis from the left would correctly determine
the direction to the source but a fish approaching from the right would think the
source was behind it. The question remains however whether such a reversal could
occur for a point monopole source due to propagation conditions alone. The typical
natural environment for the midshipman fish directionalization problem consists of
a source (the male midshipman) and receiver (the female) both located close to the
bottom in 50–100 cm depth water. This condition was generally mimicked in the
Bodega Bay experiment but the actual boundary conditions at the bottom are
unknown in both cases. The field at the receiver consists of the direct signal and
signals from multiple reflections from the surface and bottom. This problem is
extremely difficult to model because neither ray models nor normal mode models
can be used. Ray acoustics are inappropriate because the wavelength is much longer
than any other characteristic length involved and normal mode solutions cannot be
used because the waveguide has no propagating modes. The four largest terms in the
solution are the direct signal, its surface and bottom reflections, and the signal which
is reflected twice, first by the surface and then by the bottom. For a fluid-like bottom
the sum of these signals can be determined analytically (Jensen et al. 2011,
pp. 87–101). Although this solution is, at best, an approximation for the actual problem it is a solution to a real problem (two vertically aligned sources with opposite
signs, over a realizable fluid-like half-space).
Predicted values the time-averaged intensity for this model, I
v
=
( )
1
2
Re ˆ ˆ *
p
,
normalized by 1
2
1
2
ˆ
ˆ ˆ
I
v
= p versus distance from the source, are shown in Fig. 4 for
frequencies of 80, 90, and 100 Hz. The acoustic properties of the bottom are similar
to those of concrete, c = 3400 m/s, r = 1800
3
kg m
/
. The water depth is 50 cm with
the source 6 cm from the bottom and the receiver 5 cm from the bottom. The plotted
quantity, the dimensionless ratio G =
( )
Re ˆ ˆ
ˆ ˆ
*
p
p
v
v
must always fall between −1 and +1.
J.A. Sisneros and P.H. Rogers
15–20 m). In a tank experiment on midshipman directionalization (Coffin et al. 2014)
intended to approximate that environment, it was observed that females were generally able to resolve the 180° ambiguity and localize the sound source. Acoustic field
measurements in the tank and a method-of-images propagation model for the natural environment indicated that the time average intensity pointed in the wrong direction (i.e., towards the source) from a distance of 1 cm from the source out to a
distance beyond the release point, a meter from the source. This conclusion however
is called into question because the propagation model that was used has been determined to be invalid for a source and receiver so close to the bottom in such shallow
water. The field measurements in the Bodega Bay tank also indicated reversal of the
direction of the time averaged intensity vector but an erroneous phase in such measurements is always a possibility. Thus the question of whether the sign of the timeaveraged intensity could point in the wrong direction due to boundary conditions
direction remains moot. It is evident from the result shown for the point cardioid
that the sign of the time-averaged intensity can change as the field point moves
along the main response axis. Note that the intensity vector for a cardioid source
points to the left on both sides of the source in the near field (Fig. 10c) implying that
a fish approaching the source along the axis from the left would correctly determine
the direction to the source but a fish approaching from the right would think the
source was behind it. The question remains however whether such a reversal could
occur for a point monopole source due to propagation conditions alone. The typical
natural environment for the midshipman fish directionalization problem consists of
a source (the male midshipman) and receiver (the female) both located close to the
bottom in 50–100 cm depth water. This condition was generally mimicked in the
Bodega Bay experiment but the actual boundary conditions at the bottom are
unknown in both cases. The field at the receiver consists of the direct signal and
signals from multiple reflections from the surface and bottom. This problem is
extremely difficult to model because neither ray models nor normal mode models
can be used. Ray acoustics are inappropriate because the wavelength is much longer
than any other characteristic length involved and normal mode solutions cannot be
used because the waveguide has no propagating modes. The four largest terms in the
solution are the direct signal, its surface and bottom reflections, and the signal which
is reflected twice, first by the surface and then by the bottom. For a fluid-like bottom
the sum of these signals can be determined analytically (Jensen et al. 2011,
pp. 87–101). Although this solution is, at best, an approximation for the actual problem it is a solution to a real problem (two vertically aligned sources with opposite
signs, over a realizable fluid-like half-space).
Predicted values the time-averaged intensity for this model, I
v
=
( )
1
2
Re ˆ ˆ *
p
,
normalized by 1
2
1
2
ˆ
ˆ ˆ
I
v
= p versus distance from the source, are shown in Fig. 4 for
frequencies of 80, 90, and 100 Hz. The acoustic properties of the bottom are similar
to those of concrete, c = 3400 m/s, r = 1800
3
kg m
/
. The water depth is 50 cm with
the source 6 cm from the bottom and the receiver 5 cm from the bottom. The plotted
quantity, the dimensionless ratio G =
( )
Re ˆ ˆ
ˆ ˆ
*
p
p
v
v
must always fall between −1 and +1.
J.A. Sisneros and P.H. Rogers