147
pressure-response axis of the source where the particle velocity is nearly aligned
with the direction to the dipole source or site “B” which was located near the direction of the pressure node where the local particle velocity was nearly orthogonal to
the direction of the source. For the 44 females that exhibited a positive phonotaxic
response, the paths to the source were traced and analyzed (see Figures 7, 8, and 9 in
Zeddies et al. (2012)). For the 20 females released from the “A” site, females
followed “straight to slightly curved tracks to the sound source.” This is consistent
with either hypothesis. For the 24 females that were released from the “B” site
where the initial local acoustic particle velocity was orthogonal to the source direction, 19 females followed curved paths that more-or-less followed the local velocity
vectors but 5 females swam directly to the source. The authors concluded, principally from the B site results, that gravid females did not know the direction to the
source and followed the local velocity vectors. It is evident from Eq. (12) that for a
dipole source the oscillatory part of the intensity (the imaginary terms in Eq. 12) is
much larger than the steady part (the real term in Eq. 12) since kr » 0 3
. near the
release points. This results in a large signal but with ambiguous sign aligned with
the local acoustic velocity and a small but steady signal pointing away from the
source. It is not unreasonable to assume that the fish would be influenced by both
type signals. It is hypothesized here that the females were making use of the timeaveraged intensity in their approach to the source. Consider the following:
1) Five gravid females released from site “B” swam directly to the source, ignoring
the orientation of the dominant local particle velocity. Apparently, they knew the
direction to the source, and the only way they could have known it was from
direction of 〈I〉.
2) In support of their conclusions, the authors state that the fish’s path to the source
in general oscillate randomly about the particle velocity field lines. However, the
data from Figure 9 in Zeddies et al. (2012) seems to indicate that on average the
deviations from the field direction show a definite bias with respect to zero while
according to the authors’ hypothesis there would be should be no bias. The paper
does not precisely define the direction of the variations between the path and the
field lines so it is not possible to tell whether the bias is towards or away from
the source but in all three cases (release from A, release from B going to the right
and release from B going to the left) the bias, with respect to the direction to the
source is the same. Ascertaining the size and direction of the bias and its statistical significance would require a complete reanalysis of the data or, if necessary,
a repeat of the experiment. A statistically significant bias, especially toward the
source would indicate that the fish “knew” the direction to the source.
The time-averaged intensity vector points directly away from the source for freefield point monopole and point dipole sources at all ranges. It turns out that this does
not apply to all point sources. A point cardioid source provides a counterexample.
A point cardioid consists of a point monopole and collocated point dipole. The amplitude of the dipole is adjusted to equal that of the monopole in the far-field of one of
its main response directions at a certain frequency. This combination of sources
produces a cardioid shaped beam pattern with an amplitude twice that of the monoDirectional Hearing and Sound Source Localization in Fishes
pressure-response axis of the source where the particle velocity is nearly aligned
with the direction to the dipole source or site “B” which was located near the direction of the pressure node where the local particle velocity was nearly orthogonal to
the direction of the source. For the 44 females that exhibited a positive phonotaxic
response, the paths to the source were traced and analyzed (see Figures 7, 8, and 9 in
Zeddies et al. (2012)). For the 20 females released from the “A” site, females
followed “straight to slightly curved tracks to the sound source.” This is consistent
with either hypothesis. For the 24 females that were released from the “B” site
where the initial local acoustic particle velocity was orthogonal to the source direction, 19 females followed curved paths that more-or-less followed the local velocity
vectors but 5 females swam directly to the source. The authors concluded, principally from the B site results, that gravid females did not know the direction to the
source and followed the local velocity vectors. It is evident from Eq. (12) that for a
dipole source the oscillatory part of the intensity (the imaginary terms in Eq. 12) is
much larger than the steady part (the real term in Eq. 12) since kr » 0 3
. near the
release points. This results in a large signal but with ambiguous sign aligned with
the local acoustic velocity and a small but steady signal pointing away from the
source. It is not unreasonable to assume that the fish would be influenced by both
type signals. It is hypothesized here that the females were making use of the timeaveraged intensity in their approach to the source. Consider the following:
1) Five gravid females released from site “B” swam directly to the source, ignoring
the orientation of the dominant local particle velocity. Apparently, they knew the
direction to the source, and the only way they could have known it was from
direction of 〈I〉.
2) In support of their conclusions, the authors state that the fish’s path to the source
in general oscillate randomly about the particle velocity field lines. However, the
data from Figure 9 in Zeddies et al. (2012) seems to indicate that on average the
deviations from the field direction show a definite bias with respect to zero while
according to the authors’ hypothesis there would be should be no bias. The paper
does not precisely define the direction of the variations between the path and the
field lines so it is not possible to tell whether the bias is towards or away from
the source but in all three cases (release from A, release from B going to the right
and release from B going to the left) the bias, with respect to the direction to the
source is the same. Ascertaining the size and direction of the bias and its statistical significance would require a complete reanalysis of the data or, if necessary,
a repeat of the experiment. A statistically significant bias, especially toward the
source would indicate that the fish “knew” the direction to the source.
The time-averaged intensity vector points directly away from the source for freefield point monopole and point dipole sources at all ranges. It turns out that this does
not apply to all point sources. A point cardioid source provides a counterexample.
A point cardioid consists of a point monopole and collocated point dipole. The amplitude of the dipole is adjusted to equal that of the monopole in the far-field of one of
its main response directions at a certain frequency. This combination of sources
produces a cardioid shaped beam pattern with an amplitude twice that of the monoDirectional Hearing and Sound Source Localization in Fishes