An investigation of bubble resonance and its implications for sound production by deepwater fishes
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Although the continental slope and abyss comprise the largest habitat on earth, the absence of documented fish sounds from deep waters is striking. Fishes with sexually dimorphic muscles attached to their swim bladders suggests that sounds are likely used in male courtship on the upper, mid and lower continental slope. To investigate the effects of environmental extremes on fish sound production, the acoustic behavior of a driven bubble is examined. This study is also relevant to target strength of sonar returns from fish and hearing in auditory specialist fishes. A bubble is a classic, if imperfect, model for swim bladder behavior since the swim-bladder wall is an anisotropic viscoelastic structure responsible for rapid damping. Acoustic properties of bubbles–including far-field resonant frequency, damping factor, and quality factor–are calculated in warm and cold surface conditions and in cold deep-water (depths 1000 m, 2000 m, and 3500 m) conditions using parameters for oxygen and nitrogen, the dominant gases in swim bladders. The far-field resonant frequency and damping factor of a bubble increase with depth, and the scattering cross-section and quality factor decrease with depth. These acoustic properties scale with undamped oscillation frequency of the bubble and do not vary significantly due to gas type or temperature. Bubbles in the deep-water environments are much less efficient radiators of sound than bubbles near the surface because the far-field radiated power for the same excitation decreases with depth. A bubble at depth 3500 m has a 25 dB loss in radiated sound power compared to the same-radius bubble at the surface. This reduction of radiation efficiency in deep water likely contributes to the absence of fish sound recordings in those environments.
© 2022 Sprague et al. This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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Jupyter notebook with calculations of seawater and gas properties. Calculations use the Julia Programming Language  version 1.7.2.
journal.pone.0267338.s002.pdf (258 kB)
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journal.pone.0267338.s003.ipynb (3188 kB)
Jupyter notebook with calculations of bubble dynamics. Calculations use the Julia Programming Language  version 1.7.2.
journal.pone.0267338.s004.pdf (2376 kB)
PDF containing bubble dynamics calculations. PDF file created from S3 File. This file does not require Jupyter or Julia for viewing.
Originally published in PLoS One, doi: https://doi.org/10.1371/journal.pone.0267338