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A Century of Sonar: Planetary Oceanography, Underwater Noise Monitoring, and the Terminology of Underwater Sound
Even without considering extremes of high pressure, circum- stances occasionally arise on Earth that lead to the deploy- ment of a hydrophone or modeling of sound propagation in a medium of abnormally high or low impedance (Lamarre and Melville, 1994; Beaudoin et al., 2011). Transmission of sound across a boundary with a large impedance contrast then gives rise to a further ambiguity depending on whether the associated transfer function (transmission loss or propa- gation loss) is corrected for the impedance ratio (Ainslie and Morfey, 2005; Ainslie, 2008).
What Exactly is a Level?
Given that the ambiguity illustrated by Table 2 stems from the reporting of a level in decibels, the only way to resolve it, short of discarding the decibel altogether (Horton 1952, 1954, 1959; Chapman and Ellis, 1998; Clay, 1999; Hickling, 1999; Chapman, 2000), is to be more precise in our use of the decibel as a unit of level. To achieve this we first need to understand what a level is. According to ISO 80000-1:2009 ‘Quantities and Units Part 1: General’ (ISO, 2009), and ANSI S1.1-2013 ‘Acoustical Terminology’ (ANSI, 2013), a level, L, is the logarithm of the ratio of a quantity q to a reference value of that quantity q0. In equation form, L = logr q/q0, from which it is clear that the value of q (the nature of which must also be specified) can only be recovered unambigu- ously from that of L if the base of the logarithm (r) and the reference value (q0) are both known precisely.
The convention to use [1 μPa]2/ρ0C0 as a reference intensity ... is neither an American national standard nor an international standard, nor has it ever been.
Q1 What is the base of the logarithm?
ISO 80000-3:2006 (ISO, 2006) distinguishes between the level of a field quantity on the one hand and level of a power quantity on the other. In Table 1, field quantities (e.g., sound pressure) and power quantities (e.g., sound power) are iden- tified by an ‘F’ or ‘P’, respectively, in the second column. The level of a field quantity F, with reference value F0, is LF = loge F/F0, implying that, for the level of a field quantity, the base r = e. Similarly, the level of a power quantity P (reference value P0) is Lp = (1/2)loge P/P0 , from which it follows that Lp = loge2(P/P0) and therefore, for the level of a power quantity, r = e2.
For every real, positive power quantity P there exists a field quantity F = P1/2, in which case that field quantity may be referred to as a root-power quantity (ISO, 2009), and for which (assuming also that F0 = P01/2) the level LF as defined above is equal to the level LP. Further, the term “field quan- tity” is deprecated by ISO 80000-1:2009. For these reasons, attention is restricted in the following to real, positive power quantities and to their corresponding root-power quantities.
Q2 What is the reference value?
International standard reference values for selected power quantities, indicated by a ‘P’ in column 2 of Table 1, are given in column 7(q0) of that Table, and the reference value of each corresponding root-power quantity is q01/2. For ex- ample, the reference value of sound exposure, E, is q0 = 1 μPa2 s; the corresponding root-power quantity is E1/2, whose reference value is therefore q 1/2 = 1 μPa s1/2.
International standard reference values for selected root- power quantities, indicated by an ‘F’ in column 2 of Table 1, are given in column 7(q0) (remember that root-power quan- tities are also field quantities), and the reference value of each corresponding power quantity is q02. For example, the reference value of RMS sound pressure, ρRMS, is q0 = 1 μPa; the corresponding power quantity is p2= ρRMS2, whose refer- ence value is q02 = 1 μPa2.
Corollary: how large is a decibel?
16 | Acoustics Today | Winter 2015
0
Although correct (by definition), the equation Lp = (1/2)loge P/P is rarely used in that form. Instead the decibel (dB) is
0
introduced, defined in such a way that Lp = 10 log10 P/P0 dB.
It follows by equating these two expressions for Lp that the decibel is a dimensionless constant, equal to (1/20)loge 10 ≈0.115 129.
International Harmonization
Don't write so that you can be understood, write so that you can't be misunderstood. – William Howard Taft (1857-1930)
The effective communication of precise information and ideas requires a precise language. Our ability to communi- cate effectively is compromised by the ambiguity inherent in conventional reporting of levels in decibels.
widely used, primarily due to its adoption and promulgation by (Urick 1967, 1983), but it is neither an American national standard nor an international standard, nor has it ever been, and the absence of a standard value of Z0 leads to widespread ambiguity. Under normal conditions on Earth, the effects
The convention to use (1 μPa)2/Z as a reference intensity is 0