Both sound and light can be measured either in abolute terms related to the abolute power
(in watts) carried by a wave, or in "human" terms involving a simplified model of the
human senses. For light, the power "perceived" by the retina is measured in
lumens, not watts. For a pure color (single light frequency)
the two are proportional. The cofficient of proortionalitiy is called the
mechanical
equivalent of light and is equal to 638 lm/W (683
lumens per watt) at 540 THz, by definition of the lumen.
In the case of sound, one measure of power is the so-called sound intensity,
which is the physical power flowing through a unit surface.
The SI unit of physical sound intensity is the watt per square
meter (W/m2 ).
The amplitude of sound is defined in terms of pressure differences and measured in
pascals (Pa).
From a physical standpoint, sound is best described in terms of the actual
root mean square (RMS) flux of the mechanical power`
carried by a soundwave, irrespective of the ability or inability of the human ear to gauge
it in terms of perceived loudness.
If that viewpoint is adopted, then:
0 dB level (SIL) corresponds
to a sound intensity of
10-12 W/m2
That convention is preferred by physicists for theoretical computations.
The RMS power of a complicared wave is simply the sum of the RMS powers
of all its sinusoidal harmonic constituents.
Two sine waves of equal amplitude carry the same power even if they have different frequencies.
On the other hand,
a sound pressure level (SPL) of 0 dB is
attributed, by convention, to
the barely audible signal corresponding to a peak-to-peak pressure swing of
.02 mPa (20 micropascals) in dry air for a a 1 kHz sine wave.
(For water, the reference pressure swing seems [?] to be 1 micropascal.)
Peak-to-peak measurement cannot be used directly, except for a sine wave.
The power of other signals is the sum of the powers of all their harmonic
components (sinusoidal component).
Another approach exists which may assign different loudnesses
to two sinusoidal sinewaves of the same amplitude.
This attributes a conventional weight, closely related to "average" human perception,
to different tonalities. One common such scale is referred to as dB-A.
Although the dB-A weighing could theoretically be used with the
sound intensity level (SIL) defined above,
it's almost exclusively based on the sound pressure level (SPL)
defined below, for the simple reason that sound pressure
is what's actually measured physically (sound intensity is deduced).
The two sound scales (SIL and SPL) are identical in practice
(up to a tiny shift discussed below)
because the intensity is proportional to the square
of the sound pressure, except for extremely loud sounds
(which arguably don't even qualify as sound because substantial
heat is irreversibly evolved).
Thus, a 20 dB increase is either a tenfold
increase in sound pressure or a hundred-fold increase in sound intensity.
Under ordinary circumstances, sound pressure
is what's actually measured physically and sound intensity is deduced.
Either way, the measurement results corresponding to any mix of frequencies
can be reported with or without reference to actual human perception.
One common scale (closely related to some "average" human perception) is known
as "dB-A". It's opposed to the "dB-C" scale, which reports
the physical amplitudes of sounds without attempting to approximate the subjective way
people perceive loudness.
Customarily in North America, "dB-SIL" or "dB-SPL" are used to specify
precise physical measurements (with dB-C weighing)
whereas "dB-A" refers to human-perceived loudness,
often at a lesser precision.
(The latter differs greatly from the competing
standard which purports to achieve the same in metrological conditions).
Unqualified "dB" indications usually mean "dB-A"
in the audio field and "dB-SPL"
for very loud sounds, potentially damaging to human hearing
(see table).
The conversion between the SIL and SPL scales simply entails a small additive shift,
involving the logarithm of the ratio between the power flux and the square of the amplitude,
as discussed below.
The different "A-weighting" of audio frequencies takes roughly
into account the sensitivity of a "typical" young human hear.
The "dB-A" indication (sometimes pronounced "dB audio" or "dB acoustic")
bears no direct relation with the physical (RMS) scale when a wide acoustic spectrum is considered.
So, what exactly is the peak-to-peak pressure swing of a 1 kHz sinusoidal soundwave at 0 dB RMS?
Numericana :
Measuring sound in decibels
By definition, a standard atmosphere (atm)
is 101325 Pa.
Of course, a pressure disturbance whose amplitude is 2 atm peak-to-peak would not
qualify as "sound". It would not be small enough to be reversible
and it's difficult to envision how it could take the shape of a symmetrical wave, let alone a
sinusoidal one. Even if such a large disturbance was sinusoidal to begin with,
its 100% swing in relative pressure would entail a nonlinear propagation that would soon
distort it beyond recognition.
A pressure swing down to zero could be expected in the most violent
nuclear or volcanic explosions.
Realistic nonsinusoidal shapes could possibly carry slightly
more power than a sinewave with a zero minimum.
However, the latter still gives a good estimate of
the highest mechanical energy which the atmosphere of the Earth can carry away
in a "soundlike" way, namely:
194 dB-SPL = 184 dB-RMS ???
The corresponding computation which follows is a good excuse to examine
the exact basis which serves to measure the loudness of sound...
Using the "sound pressure level" (SPL) standard, the sine wave
described above has 10132500000 times the amplitude of a 0 dB sound.
It has thus a 200 dB (SPL) magnitude (more precisely: 200.114 dB).
