Page 26 - January 2007

Definitions: The use of decibel notation
We recall that decibels in acoustics were defined origi-
nally at Bell Labs as 10 times the logarithm of the ratio of the
2
sound intensity to a reference intensity. Sound intensity has
units of W/m2 and is given by
(1)
where p is the rms (root-mean-square) pressure in Pa obtained from measurements, ρ is density in kg/m3 and c is sound speed in m/s. Eq. (1) assumes that pressure is meas- ured sufficiently far from its source such that a plane wave
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approximation applies. The reference intensity for sound in
air (ρair is about 1.2 kg/m3 and cair is about 340 m/s) is
(2)
where pref-air equals 20 μPa, corresponding to the rms pres- sure at the nominal threshold of human hearing at a fre- quency of 1000 Hz. The reference intensity for sound in water (ρwater is about 1025 kg/m3 and cwater is about 1500 m/s) is
(3)
where by accepted convention, pref-water equals 1 μPa.
Note that the reference intensity levels in air and water differ by more than 6 orders of magnitude. It is this reason why air and water measurements in decibels (dB) are not the same, as the references themselves differ by 62 dB. The char- acteristic impedance of air, ρaircair, and water, ρwatercwater, have units of rayls named in honor of Lord Rayleigh. The standard characteristic impedance for air is approximately 415 rayls and for water is about 1,500,000 rayls. Impedance in acoustics is the ratio of acoustic pressure to particle velocity for plane waves. It plays the same role as resistance does in electric circuits, the ratio of voltage and current. Ohm’s law
applies to electricity and acoustics.
Sound pressure can also be expressed as a level in dB, and
consistent with the above definition regarding ratio of inten- sities, sound pressure level (SPL) in dB is thus defined as:
(4)
Equation (4) defines SPL in terms of the square of the pres- sure amplitude, and to emphasize the all-important reference pressure level, the shorthand “dB re 20 μPa2 ” is required if measurements of p were made in air and “dB re 1 μPa2 ” if they were made in water. It has, however, become convention to express the reference levels as “dB re 20 μPa” in air and “dB re 1 μPa” in water, in view of the fact that SPL in Eq. (4) can also be obtained from the ratio of rms pressures, i.e, by 20 times the logarithm of the ratio p/pref. We will also refer to SPL values in this manner.
The approximate magnitude range of the pressure spectral density for underwater ambient noise
The underwater ambient noise field depends both on the strength and density of sources of sound and on the propaga- tion to the receiver, which in turn depends on the particular underwater environment as set by sound speed, bathymetry, acoustic properties of the seabed, and ocean dynamics. We expect and indeed observe large fluctuations in the level of underwater ambient noise upon a change in time, location, or depth. Still, it is possible to sketch out a function describing the approximate magnitude range for the pressure spectral densi- ty of underwater ambient noise in very general terms. The pressure spectral density gives the mean-squared pressure of noise measured within a given frequency bandwidth, divided by the measurement bandwidth Δf, and thus the ordinate is in units of pressure squared per hertz.
For underwater acoustics, the decibel unit for pressure spectral density is dB re 1μPa2/Hz, which is called the spectral level. To obtain SPL in dB from spectral level values, a partic- ular bandwidth of interest needs to be identified. For exam- ple, if the spectral level were a constant N, over the band- width B, in Hz, SPL would be N + 10log10(B). If the spectral level is not constant over the bandwidth of interest, integra- tion of the pressure spectral density in linear units (i.e., mean square pressure per hertz) is instead performed to recover the mean-squared pressure.
The earliest studies of underwater ambient noise were made during World War II and were quite extensive, covering a wide range of locations and conditions, and were published
4,5
formed the basis of many prediction systems.
As a consequence of their location near the surface, the
radiation efficiency of both shipping and sea surface noise sources diminishes for sound rays (representing the direction of sound propagation) that have decreasing angle relative to horizontal. On the other hand, long range propagation favors ray angles close to the horizontal, and this tends to dominate in the case of low frequency, distant shipping noise. The vertical angular distribution of sound from distant shipping sources will be enhanced at shallow grazing angles, despite the fact that the initial radiation efficiency for such angles was small. Sea surface noise, however, is mainly generated by bubbles very close to the sea surface, much closer than ship noise sources. Because the sea surface is a “pressure release” surface with a substantial impedance mismatch, the radiation from the bub- bles and their surface images is effectively dipole with maxi- mum radiation downwards. As a result, most of the noise at a receiver comes from nearby sources and steep angles, often leaving a gap that is observed in the vertical angular distribu- tion near horizontal, known as the “ambient noise notch.”7
These established that surface-ship radiated noise, sea surface noise (mainly breaking waves and what was later found to be the ensuing bubble production), and the sounds of the marine ani- mals contribute most to the ambient noise field. In a later study, Wenz6 recognized that ships across an ocean basin could produce a general low frequency background noise that may not in fact be recognizable as coming from shipping; he called this “traffic noise” to distinguish it from noise from readily identifiable shipping sources. His noise summary curves have
in a substantial report and later in a scientific paper.
24 Acoustics Today, January 2007