AN INTRODUCTION TO UNDERWATER ACOUSTICSThe following is a very brief overview of the basic principles of underwater acoustics. What is Sound?A propagating sound wave consists of alternating compressions and rarefaction's
which are detected by a receiver as changes in pressure. Structures in our ears, and also
most man-made receptors, are sensitive to these changes in sound pressure (Richardson et
al.1995, Gordon and Moscrop 1996).
Note that increasing the frequency of a sound in equal steps will lead to perceived increases in pitch that seem to grow smaller with each step. For example, click on the sound frequencies below, and you'll see a more noticeable difference between 200 Hz and 225 Hz than 400 Hz and 425 Hz. 200Hz 225Hz 250Hz 275Hz 300Hz 325Hz 350Hz 375Hz 400Hz 425Hz 450Hz 475Hz Humans generally hear sound waves whose frequencies are between 20 and 20,000 Hz. Below 20 Hz, sounds are referred to as infrasonic, and above 20,000 Hz as ultrasonic. infrasonic (about 20 Hz) < human hearing < ultrasonic (about 20,000 Hz) We know a great deal about human hearing, but what about the hearing of large whales? Currently, we do not have detailed audiograms for the larger, baleen whales (note: we do have information on the hearing of smaller porpoises and dolphins from research with captive animals). Instead, we assume whales can hear the range of sounds they produce. The figure below compares human vocalizations with the sounds baleen whales are known to produce:
The Decibel ScaleIf the amplitude of a sound is increased in a series of equal steps, the loudness of the sound will increase in steps which are perceived as successively smaller. Sound intensity is generally described using logarithmic units called decibels (dB). On the decibel scale, everything refers to power, which is (amplitude)2 ; 0.0 dB corresponds to about the normal threshold of hearing and 130 dB to the point where sound becomes painful to humans.
Warning: noise levels cited in air do not equal underwater levels for reasons that will be described in the following sections. Why use the decibel scale? Because sound "loudness" varies exponentially, we'd have to deal with a lot of zeros when doing computations involving the parameters of sound, and we'd have to multiply numbers rather than simply add and subtract them. By using the decibel scale, calculations are simplified and relative values relate more closely to perception. PhaseA fourth property of sound, its phase, is less directly related to perceived sound intensity. Phase is important in describing how complex sounds can be constructed from the simple sinusoidal waves. Below is an example of two sound waves with the same frequency and amplitude - only their alignment with respect to time differs. By specifying amplitude, wavelength, and phase, any sinusoid can be exactly described. By describing these parameters for all frequency components, any complex signal can be described exactly.
Sound SpeedThe speed of a wave is the rate at which vibrations propagate through the medium. Wavelength and frequency are related by: l = c/f where lambda = wavelength, c = speed of sound in the medium, and f = frequency. The speed of sound in water is approximately 1500 m/s while the speed of sound in air is approximately 340 m/s. Therefore, a 20 Hz sound in the water is 75m long whereas a 20 Hz sound in air is 17m long. Sound PressureSound pressure is sound force per unit area, and is usually cited in micropascals (µPa), where 1 Pa is the pressure resulting from a force of one Newton exerted over an area of one square meter. The instantaneous pressure p(t) that a vibrating object exerts on an area is directly proportional to the vibrating object's velocity and acoustic impedance (rc): p(t) = rcu where r = density c = sound speed u = particle velocity Pressure can also be defined in terms of force: p = F/A where p = pressure, F = force, and A = area Sound IntensityA sound’s acoustic intensity is defined as the acoustical power per unit area in the direction of propagation: Sound Intensity (I) (W/m2) = pe /(rc) = rcu where pe or the "effective pressure" is equal to p/Ö 2 r is the density of water
and c is the speed of sound [NOTE: rc is referred to as acoustic impedance; rc in water is 1.5 x 105 (Pa ·s)/m ; rc in dry 20ºC air is 415 (Pa ·s)/m] Sound Pressure Level and Sound Intensity LevelThe sound levels to which most mammals are sensitive extend over many orders of magnitude and, for this reason, it is convenient to use a logarithmic scale when measuring sound. Both Sound Pressure Level (SPL) and Sound Intensity Level (SIL) are measured in decibels (dB) and are usually expressed as ratios of a measured and a reference level: Sound Pressure Level (dB) = 20 log (p/pref) where pref is the reference pressure Sound Intensity Level (dB) = 10 log (I/Iref) where Iref is the reference intensity In other words, the decibel is 10 times the log of the ratio of two intensities, and 20 times the log of the ratio of two pressures. The units for both SPL and SIL are dB relative to the reference intensity (often abbreviated as dB re 1µPa or dB//1µPa). Whenever "level" is added to the terms sound intensity or sound pressure, it usually implies that the measurement is in dBs. Because decibels implies a ratio of two values (and therefore a dimensionless measurement), SPL and SIL are equivalent when measured in dB. Because the dB scale is relative, reference levels must be included with dB values if they are to be meaningful. The reference levels for SPL and SIL are equivalent but are reported in different units. The commonly used reference pressure level in underwater acoustics is 1 µPa while 20 µPa (which is roughly the human hearing threshold at 1000 Hz) is used as the reference level in air. The reference intensity in water is Iref = p2 ref / (Dwater cwater) = 6.7 x 10-19 W/m2 where reference pressure in water (pref) is 1µPa rms, and the density of water (Dwater) is about 1000kg/m3, and the speed of sound in water (cwater) is about 1500 m/s. Historically, the reference intensity in air was the sound intensity barely audible to humans, 1 10-12watts/m2 or 1 pW/m2. (A painful (airborne) sound to humans = 10 watts/m2). In addition to the reference level, the distance from the source for that reference level must also be cited; typically the units of SIL are dB relative to the reference intensity at 1 meter (e.g. 20 dB re 1µPa @ 1m) (i.e. how intense the sound would be were it measured only 1m from the source). In practice, one can rarely measure source level at the standard 1m reference, so that source levels are usually estimated by measuring SPL at some known range from the source (assumed to be a single point), and the attenuation effects predicted and subtracted from the measured value to estimate the level at the reference range. Ideally, it is Sound Intensity Levels that we’d like to measure. However, it’s easier to measure sound pressure than sound intensity, so we measure pressure, and from that infer intensity. Within the same medium, sound intensity or power is proportional to the average of the squared pressure: I µ p2 therefore SIL(dB) = 10 log (I/Ir) = 10 log (p2 water / p2 ref-water) = 20 log (pwater/1µPa) In other words, once we start using the decibel scale, SIL and SPL are pretty much the same thing. Conversion of dB from air to water (and vice versa)Based on the above discussion, it should now be obvious that 120 dB in air is not the same as 120 dB in water, primarily because of the differences in reference measurements. How do we make meaningful comparisons between a ship's engine underwater and a jet engine? In air, the sound pressure level is referenced to 20 µPa, while in water the sound pressure level is referenced to 1 µPa. Given the above equation for dB's, the conversion factor for dB air è water
dB = 20 log (pwater/1µPa) = 20 log (20) = + 26 dB Therefore a pressure comparison between air and water differs by 26 dB. The characteristic impedance of water is about 3600 times that of air; the conversion factor for a sound intensity in air vs water is 36 dB. 10 log (3600) = 36 dB 36+26 = 62 dB Note that all of these conversions simply relate underwater sounds to those in air. How an animal perceives or reacts to an underwater sound may be very different from it's reaction to airborne sounds. For many marine mammals, especially the large cetaceans, there are no established audiograms - in other words, we're not sure of the hearing range of many whales. It is generally assumed, however, that animals can hear the ranges of sounds that they produce. A simplified example.... If a jet engine is 140 dB re 20µPa @ 1m, then underwater this would be equivalent to SILwater = SILair + 62 = 202 dB re1µPa To convert from water to air, simply subtract the 62 dB from the SL in water. A supertanker generating a 190 dB sound level would be roughly equivalent to a 127 dB sound in air. (Note that these are gross generalizations because the source level often changes with the frequency component of the sound.) Source, path receiver model of soundOne of the more popular models used to describe the propagation of sound through water or air is the "source, path, receiver" model (Richardson 1995). The basic parameters (there are many we will not discuss) in this model are:
A simple model of sound propagation is: SIL = SL - TL where TL = 10 log (Intensity at 1 meter/Intensity at r2 meters away from the source) Transmission loss can also be estimated by adding the effects of geometrical spreading, absorption and scattering. For our purposes we'll deal only with spreading (TLg) and absorption loss (TLa): TL = TLg + TLa where TLg = 20 log r2 (for geometrical spherical spreading; r2 is in meters) TLa = a r2 x 10-3 (units are dB/km) where a is the attenuation coefficient and a function of frequency, r2 is in meters, and 10-3 is a conversion factor for m to km Note: The rate at which sound is absorbed by water is related to the square of frequency (a µ f 2); lower frequency sounds have low absorption coefficients and therefore propagate long distances. If you know the frequency of the sound you're dealing with, the attenuation coefficient (a) can be looked up in the appropriate table or graph in any acoustics textbook. An example..... What is a humpback whale's sound intensity level at 1 km in deep water (assume spherical spreading)? source level = 150 dB re 1µPa @ 1 meter, frequency = 120 Hz therefore a ~ .003 transmission loss = TLg + TLa = 20 log (1 km) + .003(50) = 60 +.15 = 60.15 dB re 1µPa @ 1 meter. SIL = SL - TL SIL = 150 - 60.15 SIL @ 90 dB Signal to Noise RatioFinally, whether or not a particular acoustic signal can be detected in the ocean is a factor of the level of the signal of interest relative to the background noise level of the ocean, or ambient noise. This is normally expressed as a "signal to noise ratio" (SNR), where any value greater than 1 implies that the signal is detectable above the noise, while a number below 1 implies that the signal is "buried" in the noise. For rough, "back of the envelope" calculations of SNR, ambient noise level (NL) is subtracted from the sound intensity level: SNR = SIL - NL A number greater than 0 dB implies we could detect the signal from background noise, while a number less than 0 dB would imply we could not hear the signal. In the above example of the vocalizing humpback, could we hear this animal above background noise at this distance ? (assume NL at 120 Hz is about 70 dB) SNR = 90 - 70 SNR = 20 dB This whale vocalization is about 20 dB above ambient noise level, and we are likely to hear it! In practice, this basic concept becomes much more complicated. First, the ambient noise field of the ocean is quite variable with respect to time, location, and frequency. Effects can be seasonal, for example the presence of absence of a storm track that introduces loud wave noise, or hourly, such as the passing of a ship. Also, the propagation properties of the water column vary widely with location, depending on the physical oceanographic properties, local bathymetry, and bottom properties. Sophisticated numerical models have been developed over the last several decades to provide improved prediction of acoustic environmental properties. Finally, natural sound sources such as marine mammals and earthquakes, may have significant variability in their source level making the calculation of signal-to-noise ratio even more difficult. SOFAR or Deep Sound ChannelSOFAR stands for SOund Fixing And Ranging. This acronym arose when it was discovered that there was a "channel" in the deep ocean, within which the acoustic energy from a small explosive charge (deployed in the water by a downed aviator) could transmit over long distances. An array of hydrophones could be used to range on and roughly locate the source of the charge thereby allowing rescue of downed pilots far out to sea. This "channeling" of sound occurs because there is a minimum in the vertical sound speed profile in the ocean caused by changes in the density of the water column. The density is affected by water temperature, pressure (depth), and salinity. Changes in the speed of sound in the water are largely due to changes in temperature and pressure, with salinity offering only a minor effect..
Idealized profiles of temperature and pressure are shown below along
with their resulting sound speed profile: This minimum sound speed at the channel axis is the result of higher temperatures toward the surface of the ocean and higher pressures toward the bottom of the ocean. At the surface, the water temperature is relatively warm, as depth increases, temperature decreases so sound speeds decrease. At a certain depth (generally, at the bottom of or below the permanent thermocline), the water temperature is fairly uniform. At this point, the increasing pressure of the water column due to depth "takes over", and sound speeds increase due to increasing pressure. At low and middle latitudes, the deep sound channel axis is between 600-1200 m below the sea surface. It is deepest in the subtropics (about 700 m below the sea surface) and comes to the surface in high latitudes, where the sound propagates in the surface layer. Sound waves can become "trapped" in the deep sound channel and propagate long distances because they experience little attenuation beyond that due to geometric spreading and minor volume scattering in the water. To simplify, think of the water column as a layer cake with different densities of water piled on top of each other. Sound waves refract as they cross between layers of water with different densities. The refraction of sound waves from higher velocities above and below the sound channel axis bend the sound back towards the axis. Sound energy is refracted towards the axis of the sound channel away from the surface and the bottom of the ocean. Because propagating waves do not interact with either the sea surface or seafloor, sound propagating in the deep sound channel does not attenuate as rapidly as bottom- or surface-interacting paths. An example of ray paths for a source in the sound channel is shown below. Note that in
this idealized situation, the sound waves do not interact with either the surface or the
bottom. This is a simplified example of propagation in the sound channel. For a brief discussion on SOFAR, visit National Academies of Science's "Sound Pipeline".
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