Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2012;7(8):e42591.
doi: 10.1371/journal.pone.0042591. Epub 2012 Aug 9.

Angular oscillation of solid scatterers in response to progressive planar acoustic waves: do fish otoliths rock?

Petr Krysl  1 , Anthony D Hawkins, Carl Schilt, Ted W Cranford
Affiliations

Angular oscillation of solid scatterers in response to progressive planar acoustic waves: do fish otoliths rock?

Petr Krysl et al. PLoS One. 2012.

Abstract

Fish can sense a wide variety of sounds by means of the otolith organs of the inner ear. Among the incompletely understood components of this process are the patterns of movement of the otoliths vis-à-vis fish head or whole-body movement. How complex are the motions? How does the otolith organ respond to sounds from different directions and frequencies? In the present work we examine the responses of a dense rigid scatterer (representing the otolith) suspended in an acoustic fluid to low-frequency planar progressive acoustic waves. A simple mechanical model, which predicts both translational and angular oscillation, is formulated. The responses of simple shapes (sphere and hemisphere) are analyzed with an acoustic finite element model. The hemispherical scatterer is found to oscillate both in the direction of the propagation of the progressive waves and also in the plane of the wavefront as a result of angular motion. The models predict that this characteristic will be shared by other irregularly-shaped scatterers, including fish otoliths, which could provide the fish hearing mechanisms with an additional component of oscillation and therefore one more source of acoustical cues.

PubMed Disclaimer

Conflict of interest statement

Competing Interests: The authors have the following interests. Professor A D Hawkins is the Managing Director of Loughine Ltd, a company principally engaged in research activities. The company has a policy of publishing its work. Carl Schilt is owner and sole proprietor of Bigleaf Science Services in North Bonneville, Washington, USA. Bigleaf Science Services is a one-person company which, in cooperation with colleagues, publishes its work. Dr. Ted Cranford is the owner and sole proprietor of Quantitative Morphology Consulting, Inc., USA. Quantitative Morphology Consulting, Inc. is a company which, in cooperation with colleagues, publishes its work. There are no patents, products in development or marketed products to declare. This does not alter the authors′ adherence to all the PLoS ONE policies on sharing data and materials, as detailed online in the guide for authors.

Figures

Figure 1
Figure 1. The geometry of the hemispherical scatterer.
Figure 2
Figure 2. Perturbation (scattered) pressure distribution around the hemispherical scatterer at a particular time instant.
The scatterer is the void in the middle. Planar incident wave of formula image. The pressure amplitude is coded by shade, the darker the shade the higher the positive (red) or negative (blue) pressure. Level curves of pressure are also shown.
Figure 3
Figure 3. Approximate error of the normalized displacement amplitude for the spherical scatterer.
Figure 4
Figure 4. Mesh of the hemispherical scatterer located in the tank. Mesh size of 2 mm on the surface of the scatterer.
Figure 5
Figure 5. Approximate error (dashed line) and estimated true error of the longitudinal displacement of the hemispherical scatterer for the finite element solutions for excitation frequency of 100 Hz.
Figure 6
Figure 6. Simulation of hemispherical scatterer.
Illustration of the mesh with 8 element edges per radius on the surface of the domain; the surface of the scatterer is shown in solid (red) color, and the outer surface with the absorbing boundary condition is transparent (yellow).
Figure 7
Figure 7. Approximate error (dashed line) and estimated true error of the longitudinal displacement of the hemispherical scatterer for the finite element solutions for excitation frequency of 100 Hz.
Figure 8
Figure 8. Longitudinal displacement normalized by the radius of a hemisphere scatterer as a function of frequency (in terms of the parameter ).
Figure 9
Figure 9. Ratio of transverse to longitudinal displacement of a hemisphere scatterer as a function of frequency (in terms of the parameter ).
See this image and copyright information in PMC

References

    1. Webb J, Popper A, Fay R (2008) editors (2008) Fish Bioacoustics: Springer.
    1. PopperAN , Fay RR, Platt C, Sand O (2003) Sound detection mechanisms and capabilities of teleost fishes. In: Collin SP, Marshall NJ, editors. Sensory Processing in Aquatic Environments. New York: Springer-Verlag. 3–38.
    1. Carl R Schilt, Ted W Cranford, Petr Krysl, Hawkins AD (2011) Vibration of otolithlike scatterers due to low frequency harmonic wave excitation in water. J Acoust Soc Am 129: 2472–2472.
    1. Krysl P, Cranford TW, Hildebrand JA (2008) Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluids. Int J Numer Meth Engng 74: 754–775.
    1. Rodgers G (2011) An Experimental Study in Acoustically Induced Vibration of a Fish Otolith. Georgia: Georgia Institute of Technology. 59 p.

Publication types