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## The Loudest Undistorted Sound on Earth

At 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.

However, 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.

Instantaneous 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.