Oceans of noise - Whale and Dolphin Conservation Society

2.1.2. Measuring sound intensity
Ideally, acousticians would be able to measure intensity directly but practically it is easier to measure
and detect changes in pressure and then convert these to intensities. However, the use of pressure as a
measurement unit presents the acoustician with two problems, the first is related to the range of
pressure differences that the human auditory system can detect (10_Pa – 100,000,000_Pa) and the
second is related to the way in which the human auditory system processes differences in pressure, i.e.
how it judges relative loudness. The former is a practical problem where the magnitude of pressure
differences detectable by the human ear can make calculations clumsy, and the latter is a subjective
problem whereby the human auditory system processes pressure differences logarithmically and
judges these relatively. It is for these reasons that Decibel Scale and dimensionless unit the Decibel
(dB) were introduced, and the terms Sound Pressure Level (SPL) and Sound Intensity Level (SIL)
were defined.
⎛ ⎞
⎜
p
SPL( dB)
= 20log
⎟
⎜ ⎟
⎝ p dB ⋅ re.
1µ
Pa
ref ⎠
Where p is the measured pressure and pref is the reference pressure. In underwater acoustics pref water =
1µPa, in air pref air = 20µPa
⎛ ⎞
⎜
I
SIL( dB)
= 10log
⎟
⎜ ⎟
⎝ I dB ⋅ re.
1µ
Pa
ref ⎠
Where I is the measured intensity and Iref is the reference intensity. Historically, the reference intensity
(Iref) in air was the sound intensity barely audible to humans at 1000Hz, i.e. 1x10 -12 Wm -2 (1 pico Wm -
2 ). Note that if both SPL and SIL are quoted in dB they are equivalent, i.e.
⎛ I ⎞ ⎛ p ⎞
SIL(
dB)
= 10log⎜
⎟ = 20log⎜
⎟ = SPL(
dB)
⎜ I ⎟ ⎜
ref p ⎟
⎝ ⎠ ⎝ ref ⎠
From the definitions of SPL and SIL above it should be clear that decibel scale is a log ratio scale of
intensity that has dimensionless units – the decibel. It should also be clear that decibel scale
overcomes the problems discussed above, (1) ratios are a convenient way of dealing with the large
range of intensities (pressures) that the human ear can detect, (2) logarithms simplify computations
since multiplication and division are reduced to addition and subtraction, and (3) the logarithmic scale
approximates the mechanism by which the human auditory system judges relative loudness.
It is important to note the dB scale is relative and that dB values are only meaningful if a reference
level is included. The reference levels for SPL and SIL are equivalent but are reported in different
units. In underwater acoustics a reference pressure of 1_Pa is commonly used, while the reference
pressure in air is 20_Pa (this approximates the human hearing threshold at 1000Hz). The reference
intensity in water can be calculated from reference pressure by:
I
ref
⎛
= ⎜
⎝ ( ρ
p
c
medium
2
ref
medium
⎞
⎟
) ⎟
⎠
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