Of all the sensory stimuli discussed in this volume, only sound allows longrange transmission of information underwater. This is a consequence of the extraordinarily low attenuation of sound in water and the ability of sound speed gradients in the ocean to channel sound so that it can propagate without interaction with the surface or bottom.For example, as shown in Figure 5.1, at 500 Hz, which is in the middle of the hearing range for most fish, sound suffers only 1 dB of attenuation in 100 kilometers of propagation in seawater and 1 dB in 10,000 kilometers of propagation in freshwater. In comparison, at 500 Hz, electromagnetic radiation attenuates 1 dB in just I m, and blue-green light attenuates 1 dB in less than 3 m. The attenuation of sound in water is also several orders of magnitude lower than its attenuation in air, which is itself rather low.The relationships presented in the following sections are fundamental to sound fields both near and far from the source. Although the fundamental theory presented in this chapter is applicable to all ranges and frequencies, the emphasis is on true "sound" (i.e., compressional waves), rather than "hydrodynamic" (i.e., essentially incompressible) flow, which may be the dominant stimulus at close range and low frequency (see Chap. 4 for a treatment emphasizing the latter stimulus). Because of the characteristics of underwater sound propagation, fish may simultaneously receive many signals from many distances. Understanding the acoustical stimulus to the fish requires the application of these fundamental relationships. The Nature of SoundSound is a longitudinal mechanical wave that propagates in a compressible medium. By wave, we simply mean a disturbance that propagates; by longitudinal,

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A number of authors have obtained diffraction corrections for a circular piston source by numerical or graphical integration of an approximate expression for the piston field attributable to E. Lommel [Abh. Bayer. Akad. Wiss. Math.-Naturwiss. K1. 15, 233 (1886)]. Lommers expression gives the piston field in terms of trignometric functions and Lommel functions of two variables. It is shown here that the required integral of Lommers expression can be evaluated analytically to obtain a simple closed-form expression for the diffraction correction. The extrema of this expression are obtained as roots of simple transcendental equations, and approximation formulas for these roots are given. It is also shown that the same expression can be obtained by taking the limit as ka-•oo (k is the wavenumber and a is the piston radius) of Williams's exact integral expression [J. Acoust. Soc. Am. 23, 1-6 (1951)] for the diffraction correction. Finally, it is shown both analytically and by comparison with numerical values for Williams's exact expression that this simple closed-form expression is a good approximation for the diffraction correction at all distances from the source pro.vided that (ka)l/2>> 1. Subject Classification: 20.55, 20.60.

Some of the authors of this publication are also working on these related projects:ocean reverberation, seabed geo-acoustic model and seabed scattering View project International cooperation on ocean acoustics View project Naturally occurring internal solitary wave trains (solitons) have often been observed in the coastal zone, but no reported measurements of such solitary waves include low-frequency longrange sound propagation data. In this paper, the possibility that internal waves are responsible for the anomalous frequency response of shallow-water sound propagation observed in the summer is investigated. The observed transmission loss is strongly time dependent, anisotropic and sometimes exhibits an abnormally large attenuation over some frequency range. The parabolic equation (PE) model is used to numerically simulate the effect of internal wave packets on low-frequency sound propagation in shallow water when there is a strong thermocline. It is found that acoustic transmission loss is sensitive to the signal frequency and is a "resonancelike" function of the soliton wavelength and packet length. The strong interaction between acoustic waves and internal waves, together with the known characteristics of internal waves in the coastal zone, provides a plausible explanation for the observed anomalous sound propagation in the summer. By decomposing the acoustic field obtained from the PE code into normal modes, it is shown that the abnormally large transmission attenuation is caused by "acoustic mode-coupling" loss due to the interaction with the internal waves. It is also shown that the "resonancelike" behavior of transmission loss predicted by the PE analysis is consistent with mode coupling theory. As an inverse problem, low-frequency acoustic measurements could be a potential tool for remote-sensing of internal wave activity in the coastal zone.

Researchers often perform hearing studies on fish in small tanks. The acoustic field in such a tank is considerably different from the acoustic field that occurs in the animal's natural environment. The significance of these differences is magnified by the nature of the fish's auditory system where either acoustic pressure (a scalar), acoustic particle velocity (a vector), or both may serve as the stimulus. It is essential for the underwater acoustician to understand the acoustics of small tanks to be able to carry out valid auditory research in the laboratory and to properly compare and interpret the results of others.