Pressure vs. Decibels

The formula, charts and graphs on this page are meant as a resource to help show that sound is created by a vibration of air pressures. The greater the change in pressure the louder the sound. In addition to this the number of times per second that this pressure change takes place determines the frequency of the sound.

The charts have been created to help convert from decibels to various units of measure for pressure. We have included the more common ones for our example as they relate to some commonly used values. Pascals are used as they relate to atmospheric pressure and weather. Pounds Per Square Inch (P.S.I.) are used as they relate to tyre pressure amongst other things. Bar is used as it relates to turbo boost and Atmospheres (Atm) are used as they form the basis for the theoretical maximum decibel level in air.

An interesting point to note in this chart is that the relationship between pressure and decibels is based on a log 10 scale. This means that every time we increase the decibels by adding 10, we must multiply the pressure by a factor of 10. This causes immense changes in pressure over a relatively small decibel change. An example of this would be to count in a pattern as follows: 1, 10, 100, 1000, 10,000, 100,000, 1,000,000.

Have a look at the charts and graphs included and see what the corresponding pressure is for a given decibel level. Some interesting relationships exist when we see how much additional pressure is needed to gain those last few decibels.

Remember all the math classes you slept through in school? Well here is a practical use for some of those long forgotten skills.

We have discussed the idea that sound is nothing more than fluctuations of air pressure. This pressure change oscillates from positive pressure (pressurization of air) to negative pressure (rarefaction, or vacuum of air). The number of times per second that this pressure change happens determines the frequency of the sound.

It is generally agreed that the loudest sound theoretically possible in air is approximately 194dB. This corresponds to one atmosphere of pressure or 14.7psi. The reason for this limit is based on the theory that both the positive and negative portions of a sound wave must be equal, and form a perfect sine wave.

Taking this idea a step further, since the Earth has an average pressure of one atmosphere we cannot achieve anything more than a perfect vacuum on the negative side of our sound wave. Basic math shows us that:

1 Atmosphere – 1 Atmosphere = 0 Atmospheres, or a perfect vacuum.

So we are also limited to 1 Atmosphere of pressure on the positive side of our sound wave which balances things out and forms a perfect sine wave.

Understanding that sound is pressure allows us to actually show what a given Decibel rating or S.P.L. (Sound Pressure Level) is in a more familiar unit of measurement, such as Pascals (Pa) or Pounds Per Square Inch (P.S.I.)

For the enthusiast it should be noted that even though the overall pressure level may seem low until approximately 170dB we must remember that this pressure change happens many times per second on both the positive and negative sides of the sound wave. For example 194dB = 14.7psi of pressure therefore +14.7psi on the positive side and –14.7psi on the negative side of the sound wave, giving a total pressure change of 29.4psi. Furthermore this pressure change happens anywhere from 20 to 20,000 times per second!!!

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