first glance, the highest imaginable sound pressure at sea level in our
atmosphere with its average static pressure of 101325 Pa would range
from 0 Pa (a vacuum at the trough of the wave) to twice the atmospheric
pressure (crest of the wave). The amplitude of such a massive sound
wave would equal the static pressure itself.
Put in relation to the reference sound pressure of 20 μPa for 0 dB SPL, this would yield an SPL of 20 log (101325 / 20e-6) = 194 dBSPL.
The RMS value of a sinusoidal wave is 3 dB lower than its peak
amplitude, so we have to subtract 3 dB to arrive at 191 dBSPL if we
consider a sine wave.
this simplified contemplation disregards the thermodynamic properties
of the air, which is actually a non-linear medium for sound wave
propagation. At sound levels below our pain threshold, the pressure
fluctuations are small in relation to the static pressure, so the
non-linearities can be considered to be negligible. However, at SPLs
well over 150 dB, we are getting progressively into the regime of
non-linear acoustics. In adiabatic conditions, compressing the air leads
to a rise of temperature which in turn increases the speed of
propagation. This means that a sinusoidal sound wave travels faster
towards the crest than away from it, distorting the wave form towards a
saw-tooth; equivalent to introducing new frequency components which
weren’t present in the source signal. So even if the PA industry were
able ot provide sound reinforcement systems capable of creating clean
sine waves at such levels, by the time the waves reach our ears, they
would be distorted. In practice, PA manufacturers sometimes indeed have
to cope with non-linear acoustics, for example at the mouth of
compression drivers where SPLs of over 150 dB are not uncommon near the
full output level of a horn-loaded tweeter.
pressure levels far beyond the 194 dB limit exist. Thunder, bombs, and
volcanic eruptions can create shock waves with peak values much higher
than twice the static pressure. As the trough of the wave cannot go
below 0 Pa, a DC component is superimposed on these waves – equivalent
to throwing the air molecules (and anything else) far away from the
epicenter of the explosion with supersonic speed. ... but shock waves
are not considered to be sound waves.