# What is the loudest possible sound?

For a long time, Wikipedia has said that the loudest possible sound is 191 dB SPL, as this corresponds to 1 atmosphere of pressure peak-to-peak, and anything above this would be clipped at vacuum on the negative peaks, and is therefore classed as a "shockwave" rather than "sound". (Though Wikipedia also defines a shock wave as a wave moving faster than the speed of sound, regardless of amplitude.)

It gives no references, however, and I've since learned that pressure waves in air are always non-linear, and the science of acoustics assumes linearity and small pressure levels to simplify calculations. So the air will already be distorted before this pressure level.

So is there a commonly-held definition of when distortion becomes too great to consider a wave "sound"? At what dB SPL is it? Is it possible to calculate the amplitude that a sine wave in air would be distorted by 1% THD, for instance?

The "commonly held definition" is the wikipedia one... it's not so much a question of distortion, as a question that a wave is symmetrical - that is, it should not result in a net motion of gas. It is possible to construct a sinusoidal pressure wave with a peak pressure of 2 atm and a valley of 0 - from a displacement perspective this is a distorted wave, but from a pressure perspective it is not.

However, you cannot do that if the peak pressure is greater than 2 atmosphere.

• What do you mean by "from a displacement perspective"? – endolith Jan 6 '17 at 21:01
• @endolith If the sound frequency is high enough to consider the motion of the gas is adiabatic, then $PV^\gamma = \text{constant}$ where $\gamma = 1.4$ for air, so the velocity (and hence the displacement) is not a linear function of the pressure. For "normal amplitude" sound waves there is only a small change in $P$ about its mean value. Of course for a low frequency, high amplitude sound wave, the adiabatic assumption may not be strictly valid because of heat conduction in the gas. – alephzero Jan 6 '17 at 23:52
• Is it possible to calculate distortion percentage of displacement wave for a given SPL? – endolith Jan 7 '17 at 0:28