# Sound Pressure

When a sound propagates in air, the air is the medium, and the sound wave propagates by repeating the compression and rarefaction of the air. Thus, air particles in a particular region are compressed at one moment, and the air pressure increases at that place and time. On the other hand, air particles in a different region are rarefied at a different moment, and the air pressure decreases at that place and time. If there is no sound, the air pressure equals the atmospheric pressure at any given region. However, if a sound exists, there are high-pressure regions and low-pressure regions in the medium, and the pressures change. The pressure change from the atmospheric pressure is called sound pressure, and the unit of sound pressure is Pascal (Pa).

We can perceive a sound as soft as 20 μPa and as strong as 20 Pa. For expressing this wide dynamic range, “sound pressure level,” defined in the following equation, is often used:

$$\mathrm{Sound \ Pressure \ Level} = 20\log_{ 10 } \frac{p}{ p_{0} }[dB]$$

where $p$ is the sound pressure of the interest, $p_{0}$ is the reference pressure of 20 μPa, and the unit is the decibell (dB).

1. Speaks, C. E., Introduction to Sound: Acoustics for the Hearing and Speech Sciences, Singular Publishing, San Diego, CA, 1999.