# Pressure, Power, and Intensity

Written by Travis M. Moore
Lasted edited 22-Sep-2019

### Sound Pressure

How is it possible to quantify "how much" sound is given off from a particular sound source (e.g., a speaker)? Viewing sound as a series of pressure changes (i.e., condensation and rarefaction), it stands to reason that measuring sound levels must involve measuring pressure.

Fortunately, general physics already provides explanations for several physical quantities that will be necessary to measure sound. Let's walk through some basics so we get a better idea of what pressure actually is. We'll need some way to describe the fact that sound travels (propagates).

For sound, the focus is on the displacement of air molecules. Next we need to describe how quickly or slowly the displacement happens.

But molecule displacement can happen at different velocities over a given amount of time (e.g., sometimes running, sometimes walking while running a marathon). This change in velocity over time is referred to as acceleration.

Acceleration is a measure of the change in velocity, which describes the amount of displacement over time. We now have a way to measure the movement of air molecules, and capture any changes in speed of movement along the way. The next step is to apply the concept of acceleration to an actual object (e.g., an air molecule). But what are objects made of?

We're one step away from a major breakthrough! But first we have to define the relationship between how quickly an object is displaced and how massive it is.

At last we arrive at pressure! Pressure certainly is involved with force, because it takes energy to put air molecules in motion. Measuring just how much force is required to move a molecule seems like a legitimate way to quantify sound. There's just one problem with our definition of pressure as it stands: how many molecules are we measuring? One? A thousand? We need to add a defined space to our measurement.

Finally we have built a way to refer to the condensation and rarefaction that occurs from a vibrating source. Specifically, we can say that pressure is a measure of the amount of force expelled over a certain area. In acoustics, the convention is to use a square meter (m2) as the measurement area. Therefore, the unit of measuring raw sound pressure is Newtons per meter squared (NT/m2), otherwise referred to as the Pascal (Pa).

### Sound Power and Intensity

Pressure is one way to measure sound, but we can also quantify sound by referencing its power. In order to understand power we need to add the concept of "work."

Recall that force is directly related to the acceleration of a mass, so work describes the amount of force needed to move a mass a given distance. This brings us to the concept of power.

Sound power then, is the amount of work done to the molecules of air per second. In other words, how much force was exerted in moving the mass of the air molecules in 1 s. So a measure of acoustic power takes into account the movement of all the air molecules moved by a sound source.

In order to make an accurate measurement of power, we need to know where to measure in relation to the vibrating body. Do we need to measure the molecules above the sound source? Below it? In essence, what we need to know is the shape of the pressure wave created by a source. Figure 1 below shows a 2D animation of a pressure wave.

From Figure 1 we can see that sound propagates in all directions. In fact, sound propagates in a 3-dimensional sphere, away from the source. The sphere continues to expand, exerting less power the further it travels from the source, until it dissipates. So measuring sound power would mean measuring the work done to all the air molecules surrounding the sound source. However, we're not always interested in the total sound power. For example, if we need to quantify the sound emitted by a speaker, it is not really relevant how much sound is emitted behind the speaker, where no one will be listening to it. Instead, we might just want to know how much sound is being produced in front of a speaker pointed at an audience. For this narrower measure, we use sound intensity.

So while sound pressure is force per m2, sound intensity is the power per m2. Both quantities are routinely used in quantifying sound, but audiologists will most often deal with sound pressure.