This article was written by Dr. Burt Stumpf, an emeritus professor of physics at Ohio University in Athens. He is an active member of the Acoustical Society of America and the AAPT. His B.S. is from Kent State, M.S. from Michigan, and Ph.D. from the Illinois Institute of Technology. Burt has taught undergraduate and graduate courses in physics and published research in acoustics. Analytical Acoustics is a textbook he wrote also.

The ocean has become very important to us today in commercial ways - fishing, mining, oil prospecting, shipping, etc. These commercial activities in many cases involve and use the knowledge of the physical, chemical, biological and geological aspects of the ocean. A knowledge of underwater sound propagation can be helpful here. Because sound is reflected by changes in media (water to mud on the sea bottom, water to air at the surface, water to objects in the ocean) and refracted by changes in temperature of the seawater, salinity and depth or pressure, it can be used in studies of the ocean's physical characteristics. For example, the bottom topography can be studied by sonar (underwater sound). Sonar is an acronym for sound navigation and ranging. Sound studies can also give us information of a biological nature. For example, the depth of schools of fish can be determined by the transit time for sound emanating from a sonar transducer on a ship and returning after reflection from the fish.

Only a brief discussion of some of the highlights of underwater sound are presented. These include comparisons of water with air as an acoustic medium; echo ranging; and refraction, scattering and absorption of sound in the sea.

1. Comparison of the Acoustic Properties of Water with Air
   There are several differences for sound propagation in water compared with air. The speed of sound in water is 1481 meters/second at 20⁰C and for air is 343 m/sec at 20⁰C. Underwater sound projectors have to be larger for a given frequency than projectors in air to produce the same narrow radiation patterns. Refraction is very important for propagation in water. Sound absorption is less in water. Sound channels can be important in water also. Sound speed in seawater depends on pressure, temperature and salinity.
2. Echo Ranging to Detect and Locate Objects
   Echo ranging involves the determination of the direction and distance (by sound transit time) to underwater objects such as fish, submarines, etc. By this method pulsed sound is sent out and its echo received. The direction of the object is associated with the direction of the largest received echo signal and the distance is associated with the transit time for the pulse. The strength of the echo is determined by:
   1. the inverse square law spreading;
   2. the size and the characteristic impedance or reflection coefficient of the target object, which are associated with the target strength;
   3. the loss due to refraction by temperature gradients, pressure gradients, etc;
   4. the absorption in seawater (due to viscous and relaxation mechanisms);
   5. the directivity pattern of the transducer; and
   6. the intensity of the projected sound from the source.
3. Refraction of Sound in the Ocean
   The velocity of sound in seawater depends on temperature, depth or pressure, and salinity, as mentioned. The temperature and depth dependence is, in approximation to Wilson's equation, [1] (see References)
   c = (1,449 + 4.6 t + 0.017 h) m/sec
   where t is in degree centigrade and h is depth in meters. Introductory physics textbooks discuss the reflection and refraction (bending) of light rays at boundaries. The same laws (reflection and Snell's) hold for sound waves. The rule is that the ray bends away from the normal to the boundary if the velocity increases in the second medium and bends toward the normal if the velocity decreases in the second medium.
   It is shown [2] that for a constant velocity gradient with depth in m/sec per meter the ray is a circular arc with a radius, R, given by R = C₀ / G , where C₀ is the velocity at the source and G is the velocity gradient. The direction of bending depends on the signs of G.

   Scattering of Sound in the Ocean
   When sound propagates in the ocean, it can be scattered from the ocean surface, the bottom and from scatterers in the volume, such as fish or marine life or temperature discontinuities. The discontinuities in impedance caused by these aspects of the ocean mentioned are important for the sound scattering back to the sound source. The analysis of the scattered signal (often by advanced mathematical techniques - autocorrelation, Fourier transforms, etc.) can give good information about the sound scatterer.

   Absorption of Sound in the Ocean
   The absorption of sound in seawater depends on the temperature and frequency. For example, the absorption coefficient is 0.9 dB/kyd at 10,000 Hz and 15⁰C. Several processes cause the absorption of sound in seawater, each having a distinct frequency dependence. The expression for the absorption in water is

   I (r) = I₀ e^-2ar
   Here I(r) is the intensity at distance r from the source, I⁰ is the source intensity, a is the absorption coefficient.

1. F.B. Stumpf, Analytical Acoustics, Chapter 9. (Most of the material in this newsletter article came from this book.)
2. Acoustics Source Book, McGraw-Hill Co., pp. 93-104.
3. D. Tucker and B. Gazey, Applied Underwater Acoustics.
4. W.W. Seto, Acoustics, Chapter 8. This is a book in the Schaum's Outline Series. L. Kinsler, A. Frey, A. Coppens and J. Sanders, Fundamentals of Acoustics, 3rd Edition, Chapter 15.
   [1] Wilson, W. J. Acoust. Soc. Am. 32:1357 (1960).
   [2] Seto, W.W. Acoustics (New York: McGraw-Hill Book Co., 1971), p. 174.