Shallow-water Acoustics and Relevant Physics By: Elizabeth Frontage Underwater Acoustics is a complex phenomenon. Leonardo dad Vinci simplified the concept in 1940, two years before Columbus discovered America, by saying “If you can cause your ship to stop and place the head of a long tube in the water and place the outer extremity to your ear, you will hear ships at a great distance from you. ” (5, p. 2) There are many factors that contribute to the complexity of underwater acoustics and sonar.
In the ocean things such as sound transmission losses in sea water, refraction phenomena, sound channels, influence of surface reflection on remission loss, bottom reflection phenomena, source level, factors influencing echo levels, masking by noise, masking by reverberation, and acoustic outputs of ships all have to be taken accounted for (2). Shallow water is also usually a noisy environment because shipping lanes exist along coastlines. We are going to examine a few of these effects and see the direction that the developments in underwater acoustics may lead, as well as focusing on some military applications of sonar.
We are going to start by looking at the history of underwater acoustics from a military standpoint to understand its purpose and realistic applications. The first quantitative measurement in underwater sound was in 1827 when Daniel Celadon and Charles Strum collaborated to measure the velocity of sounds in Lake Geneva in Switzerland. By timing the interval between a flash of light and the striking of a bell underwater, they determined the velocity of sound to a surprising degree of accuracy. (5, p. ) By the turn of the century there was the first application for underwater sound, the submarine bell. By timing the interval between the sound of the bell and the sound of a simultaneously sent blast of a foghorn, a ship could determine its distance from the lightship where both were installed. The system was the momentum for the founding of the Submarine bell by the Submarine Signal Company, or SC, the first commercial manufacturer of sonar equipment in the United States. (5, p. 3) In 1912, 5 days after the “Titanic”, L.
F. Richardson filed a patent application with the British Patent Office for echo ranging with airborne sound but he did nothing to implement his proposals. (5, p. 3) Meanwhile, R. A. Possessed, from the US, designed and built a new kind of moving-coil transducer for both submarine signaling and echo ranging and was able to detect an iceberg at a distance of 2 miles by 1914. 5, p. 3) These transducers are said to have been installed on all US submarines of the WWW period to enable them to signal one another while submerged.
The outbreak of World War I in 1914 was the incentive for the development of a number of military applications of sonar. In France, Childishly an engineer and Language a physicist experimented with an electrostatic condenser and a carbon-button microphone placed at the focus of a mirror and by 1916 they could obtain echoes from the bottom 1918, for the first time, echoes from submarines were heard, sometimes up to a distance of 1 500 meters. (5, p. ) However, World War I came to a close before underwater echo ranging could make any contributions.
By 1935 several fairly adequate sonar systems had developed and by 1938 with the imminence of World War II quantity production of sonar sets started in the United States. (5, p. 5) By the time the war began, a large number of ships were equipped for underwater listening and echo ranging. However, early shipboard echo-ranging sets installed in the late ass’s and early ass’s were unreliable in performance. Good echoes were found in the morning but not in the afternoon. It wasn’t the sonar operators themselves, it was mound that the echoes were actually weaker in the afternoon. 5, p. 5) This is because in the warm upper layer of the ocean, sound is refracted toward the surface. As sound waves travel deeper into colder water, they slow down and are refracted towards the seafloor, creating a shadow zone in which a submarine can hide. How all of these tie together will be mentioned later on. Most of our present concepts as well as practical applications had their origins in this period such as acoustic homing torpedoes, acoustic mines, and scanning sonar sets.
Factors such as target strength, he noise output of various classes of ships at different speeds and frequencies, reverberation in the sea, were all first understood around the time of World War 11. (5, p. 6) A few things that are still being researched on now are spectrum crowding, and the detection of submarines in shallow water, which is what we are going to focus on. This is because a lot of research has been done in deeper waters of the ocean, but not enough has been done in the more shallow waters and this is due to things that will be mentioned shortly.
Transitioning more the factors of underwater acoustics, we break it down to the bare minimum. The sound speed in water is about 1500 m/s, so wavelengths of interest are on the order of a few meters. In shallow water, with boundaries formed by the surface and the bottom, the typical depth-to-wavelength is about 10-100. The surface and the ocean’s index of refraction have a spatial and time dependence, and the presence of ocean in-homogeneities and loud ships can frequently scatter, Jam, or mask the most interesting sounds. (3, p. 5) Scientists are concerned with the physics of extracting a signal that propagates in a dynamic waveguide from noise influenced by that same waveguide’s complexity. The ocean can be essentially treated as a frozen medium, because the motions of ocean waves and water masses, along with the sources and receivers of signals that pass through them, are so small compared to the speed of sound in the ocean. So, temperature (In C) provides an excellent characterization of sound speed, c, because the depth plays a minor role in shallow water and the equation can be written: Czech+4. 6TH+1. 34-0. 01 TTS-35+O. Oz where the depth z is in meters, S is in salinity in parts per thousand, and the last term embodies density and static pressure effects. (3, p. 5) Seeing what goes into the characterization of sound speed, we are going to focus on depth and temperature because they are the biggest contributors, and frankly more easily explained in a minimalist fashion. Three models of the speed of sound c(z) in seawater encompass a wide variety of shallow-water oceanography. Figure [ 1 ] (From Superman, Lynch) mixed temperature conditions found during the winter in Earth’s mid latitudes and in water shallower than about 30 meters. B) The common three-layer model consists of two separate mixed layers, both of constant temperature and sound speed, with a hero cline gradient sandwiched in between. (c) In a coastal front model, two water masses with differing temperature profiles meet at a vertical wall (green). Note that the ocean bottom has a higher sound speed and density, indicated by its shift to the right, than the water layer. (3, p. 56) The waveguide in shallow water has a constant sound speed, mirror reflection at the surface, and a grazing-angle-dependent reflectivity at the ocean bottom.
A simple way to describe this is that the angle between the sound wave and a line at 90 degrees is the angle that the sound wave will travel after reflecting from the bottom. The classic plane-wave Raleigh-reflection coefficient, can similarly describe reflection from the bottom interface. The interface has a critical angle CE-?typically about 1 50, depending on the material there. Figure [ 2] (From Superman, Lynch) As shown in the upper panel of the figure, a source in such a waveguide produces a sound field that propagates at angles confined to a cone of sec.
Within that cone, constructive interference selects discrete propagation angles; outside the cone, waves disappear into the bottom after a few reflections. (3, p. 57) Solutions of the Hellholes equation, which describes waveguide propagation, are reduced using separation of variables. Going through separation of variables in this paper is not efficient, but if one wants to know they may perhaps want to take a class in partial differential equations. The depth equation is an generally problem that yields a set of normal modes satisfying the preceding boundary conditions.
When combined with the range solution, the modes propagate along the waveguide and spread cylindrically. As seen in the bottom figure, the area shaded in the “bottom” of the ocean is the amount of sound lost due to the attenuation of the way hat the sound travels. Continuing with waveguides, the figure below shows the behavior of a sound wave excited by a point source in a waveguide. Figure  (From Superman, Lynch) The propagating normal modes have different frequency-dependent group speeds, so a finite-bandwidth pulse disperses as it propagates down the waveguide and passes an array of detectors.
The lower modes become trapped toward the bottom of the waveguide because sound paths bend toward regions of lower sound speeds. The lowest mode has the most direct path down the waveguide and arrives at the detectors first. Higher modes follow and refract higher in the water column’s thermo cline. (3, p. 57) It is possible to reconstruct and focus the original sound back to its original location by time reversing the signal by transmitting the last arrivals first and the first arrivals last.
Using this, it is easy to see how following sounds transmitted by a submarine can be used to find its exact position. Using the information that has been given thus far, military applications then military). In the past, both active and passive sonar have been used. Passive sonar takes the approach of listening and exploiting the relevant physics. It only receives a signal, and is used mainly for antisubmarine warfare and to study ocean biology. Figure 4 shows a submarine that uses a passive sonar array, which is simply a long antenna towed behind the submarine, to detect a complicated mixture of sounds.
Figure 4 (From Superman, Lynch) Compared to passive sonar, active sonar sends out pulses and examines and extracts information from their echoes shown in figure 5. Figure 5 (From Superman, Lynch) For both active and passive sonar, the proximity and complexity of the boundaries, and the oceanography in shallow water influence the sonar’s performance. In addition to antisubmarine warfare, active sonar are useful in, for example, communications, mine hunting, archaeological research, imaging of ocean and seabed features, and finding fish.
One non-antisubmarine warfare application is to image internal-wave fields in the ocean using sound scattered from zooplankton that drift with the mapping ocean floor water. Based on the Doppler shift of the returned echo, the water velocity can be mapped as a function of its position. In active sonar systems, it’s allowing oceanographers to accurately map the ocean floor. (3, p. 56) Further research in shallow-water acoustics is quite necessary, for the Navy plans to counter the possible shallow-water submarine threat.