Pro Tools 101 Official Courseware is a little confused about decibels

It was pointed out by a student of Audio Masterclass that Pro Tools 101 Official Courseware Version 8 contains a rather confusing statement. In Chapter 1: Getting to Know Pro Tools, in the paragraph headed Amplitude, it says…

“Doubling the intensity of sound-pressure variations creates a gain of 3 dB”

This is neither correct nor incorrect because it is entirely nonsensical.

A doubling of sound intensity does indeed relate to a gain of 3 dB. However, a doubling of sound pressure relates to a gain of 6 dB. Sound intensity and sound pressure are two different things, so to talk about “the intensity of sound pressure” has no meaning.

The relationship between sound pressure and sound intensity is an age-old issue that commonly causes confusion. And even people who fully understand it are occasionally prone to 'slip-of-the-tongue' errors.

It is easier to start the explanation in electrical terms…

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• 6 dB represents a doubling of voltage.
• 3 dB represents a doubling of power

The reason for this is that power = voltage squared divided by resistance…

P = V2/R

It is the squaring of the voltage in this equation that causes the difference in decibel terms.

If you raise the signal level by 6 dB on a mixing console fader, you are doubling the voltage sent to the monitor loudspeakers, and at the same time you are quadrupling the power (because of the squared term).

If you raise the fader by 3 dB, then you increase the voltage by a factor of 1.414, and double the power.

Thinking now about sound traveling in air…

• Sound pressure is analogous to electrical voltage
• Sound intensity is analogous to electrical power

So if sound pressure rises by 6 dB, at the same time sound intensity rises by 6 dB. But where sound pressure is doubled, sound intensity is quadrupled.

Where the book talks about “Doubling the intensity of sound-pressure variations”, it is VERY confusing to mix intensity and pressure in this way.

Sound pressure is a measure of how hard air molecules are pressing against each other and is measured in newtons per square meter (or pascals, where one pascal = one newton per square meter).

Sound intensity is a measure of rate of energy transfer (i.e. power) and is measured in watts per square meter.

'Amplitude' can be thought of as 'size', and the way it is commonly used is as vague as that. You will therefore see references to the amplitude of sound pressure, or amplitude of sound intensity. If you think of it as a casual reference to size or magnitude, that will usually be sufficient.

More confusion

It isn't only this Pro Tools guide that is confused. Here is a statement from the website of Indiana University…

“Amplitude is directly related to the acoustic energy or intensity of a sound.”

It is difficult to read this in any way other than energy and intensity are equivalent.

This is not so. Sound intensity is a measure of power. Power is the rate of energy transfer.

It would not be hard to find other examples confusing sound pressure and sound intensity, and energy and power. Indeed, it is almost impossible to find a textbook that is perfect in every detail. The solution is to gain knowledge from multiple independent sources and, when in doubt, raise your hand and ask.

By the way, Indiana University's website also states that, “An energy transfer of one watt per second is equivalent to a Joule”. In fact one watt is equivalent to an energy transfer of one joule per second.” It's the other way round to what their website states. Having said that, I appreciate that these 'slip-of-the-tongue' mistakes are incredibly easy to make.

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