3.6: Sound in the Ocean
- Page ID
- 30041
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Sound provides the only convenient means for transmitting information over great distances in the ocean. Sound is used to measure the properties of the sea floor, the depth of the ocean, temperature, and currents. Whales and other ocean animals use sound to navigate, communicate over great distances, and find food.
Sound Speed
The sound speed in the ocean varies with temperature, salinity, and pressure (MacKenzie, 1981; Munk et al. 1995: 33):
\[\begin{array}{l} C &= 1448.96 + 4.591 t − 0.05304 t^{2} + 0.0002374 t^{3} + 0.0160 Z \\ &+ (1.340 - 0.01025 t)(S - 35) + 1.675 \times 10^{-7} Z^{2} - 7.139 \times 10^{-13} t Z^{3} \end{array} \nonumber \]
where \(C\) is speed in m/s, \(t\) is temperature in Celsius, \(S\) is salinity (see Chapter 6 for a definition of salinity), and \(Z\) is depth in meters. The equation has an accuracy of about 0.1 m/s (Dushaw et al. 1993). Other sound-speed equations have been widely used, especially an equation proposed by Wilson (1960) which has been widely used by the U.S. Navy.
For typical oceanic conditions, C is usually between 1450 m/s and 1550 m/s (figure \(\PageIndex{1}\)). Using Equation \((\PageIndex{1})\), we can calculate the sensitivity of \(C\) to changes of temperature, depth, and salinity typical of the ocean. The approximate values are: 40 m/s per 10\(^{\circ}\)C rise of temperature, 16 m/s per 1000 m increase in depth, and 1.5 m/s per 1 increase in salinity. Thus the primary causes of variability of sound speed is temperature and depth (pressure). Variations of salinity are too small to have much influence.
If we plot sound speed as a function of depth, we find that the speed usually has a minimum at a depth around 1000 m (figure \(\PageIndex{2}\)). The depth of minimum speed is called the sound channel. It occurs in all oceans, and it usually reaches the surface at very high latitudes. The sound channel is important because sound in the channel can travel very far, sometimes halfway around the earth. Here is how the channel works: Sound rays that begin to travel out of the channel are refracted back toward the center of the channel. Rays propagating upward at small angles to the horizontal are bent downward, and rays propagating downward at small angles to the horizontal are bent upward (figure \(\PageIndex{2}\)). Typical depths of the channel vary from 10 m to 1200 m depending on geographical area.
Absorption of Sound
Absorption of sound per unit distance depends on the intensity \(I\) of the sound: \[dI = -k I_{0} \ dx \nonumber \]
where \(I_{0}\) is the intensity before absorption and \(k\) is an absorption coefficient which depends on frequency of the sound. The equation has the solution: \[I = I_{0} \exp (-kx) \nonumber \]
Typical values of \(k\) (in decibels, or dB, per kilometer) are 0.08 dB/km at 1000 Hz, and 50 dB/km at 100,000 Hz. Decibels are calculated from: \(dB = 10 \log \left(I/I_{0}\right)\), where \(I_{0}\) is the original acoustic power and \(I\) is the acoustic power after absorption.
For example, at a range of 1 km a 1000 Hz signal is attenuated by only 1.8%: \(I = 0.982 I_{0}\). At a range of 1 km a 100,000 Hz signal is reduced to \(I = 10^{-5} I_{0}\). The 30,000 Hz signal used by typical echo sounders to map the ocean’s depths are attenuated little going from the surface to the bottom and back.
Very low-frequency sounds in the sound channel, those with frequencies below 500 Hz, have been detected at distances of megameters. In 1960 15-Hz sounds from explosions set off in the sound channel off Perth Australia were heard in the sound channel near Bermuda, nearly halfway around the world. Later experiment showed that 57-Hz signals transmitted in the sound channel near Heard Island (75\(^{\circ}\)E, 53\(^{\circ}\)S) could be heard at Bermuda in the Atlantic and at Monterey, California in the Pacific (Munk et al. 1994).
Use of Sound
Because low-frequency sound can be heard at great distances, in the 1950s the U.S. Navy placed arrays of microphones on the sea floor in deep and shallow water and connected them to shore stations. The Sound Surveillance System SOSUS, although designed to track submarines, has found many other uses. It has been used to listen to and track whales up to 1,700 km away, and to find the location of sub-sea volcanic eruptions.