This seemingly simple question is actually quite fundamental. To answer the question we need to consider sound intensity. Now sound intensity is defined as “the average rate of flow of energy through a unit area normal to the direction of wave propagation”. The average rate of flow of energy is energy per second which we recognise as power in Watts. Intensity then has units of Watts per square metre as it has dimensions of power transmitted per unit area. We could also define in old fashioned units like and so on, but it is better to stay with Watts. Just in case you want a modern reference note that
Now the reference for Watts in air was defined as , which at the time was considered as the intensity of a just barely audible 1kHz tone to a normal human ear. This seems a reasonable choice as we are usually dealing with sound which is definitely audible, and often annoyingly so.
Moving on if we consider either plane or spherical acoustic waves in perfect free field conditions, that is a situation where no reflections occur, then it is straight forward to show that the intensity is given by
where $p$ is the peak pressure of the sound wave, is the air density and is the speed of sound in air. Now for a sine wave
so we have
If we take the dB level we have
Now in air is approximately 400 and we have
So we can write
That is by using 2 x 10-5 as the reference we are relating the rms pressure to the barely audible intensity in a free field, or conversely a pressure of 2 x 10-5 is the sound level we can just hear at 1kHz
In normal measurements we are not in perfect free field conditions, so the dB level of the pressure is referred to as the Sound Pressure Level, namely
If the rms pressure used is over the entire frequency range then we have the Overall Sound Pressure Level, often just called the Overall Level. If the rms pressure is the output of say a third octave filter then we call it the dB Band Level at that third octave centre frequency.
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Dr Colin Mercer was formerly at the Institute of Sound and Vibration Research (ISVR), University of Southampton where he founded the Data Analysis Centre. He then went on to found Prosig in 1977. Colin retired as Chief Signal Processing Analyst at Prosig in December 2016. He is a Chartered Engineer and a Fellow of the British Computer Society.