This article highlights the main differences between the three acoustic terms: sound pressure, sound power, and sound intensity. The article attempts to explain when to use them, their units of measure, and how they relate to each other.
Article Contents: 1. Background and Decibels 2. Pressure, Power, and Intensity: Heater Analogy 2.1 Sound Pressure and Temperature 2.2 Sound Power and Heater Power 2.3 Sound Intensity and Heat Flow 3. Relationship of Sound Pressure, Sound Power and Sound Intensity 3.1 Sound Pressure and Sound Intensity Relationship 3.2 Sound Intensity and Sound Power Relationship 4. Conclusion
1. Background and Decibels
These three terms all measure different aspects of sound, but can all be expressed in decibels as shown in Figure 1. A decibel is not unit of measure, but rather a logarithmic ratio between two numbers (a measured quantity and a reference number).
Figure 1: Sound pressure, sound power and sound intensity can all be expressed in decibels (dB) even though they represent different measured quantities.
The measurement units used in sound pressure, sound power, and sound intensity are different. Often the measurement unit is omitted during discussions, and only the term “decibels” is used. This can cause some confusion to arise.
2. Pressure, Power, and Intensity: Heater Analogy
An analogy between a heater placed in a cold room, versus a sound emitting object in quiet room, can be used to illustrate the differences between pressure, power and intensity. There are several similarities between heat and sound as shown in Figure 2.
Figure 2: Heater analogy for Sound Pressure, Sound Intensity and Sound Power
The heater creates heat, which spreads throughout the room. A noise emitting object creates sound in a similar fashion. The following parallels can be drawn:
2.1 Sound Pressure and Temperature
At every position in the room, there is a specific temperature level, which is measured in degrees. Likewise, at every position in the room with the sound source, there is a particular sound pressure level, which is measured in Pascals. As heat is produced, the temperature level is higher closer to the heater. Like temperature, the sound pressure level is typically higher closer to the noise emitting object. Both the sound pressure level and temperature level are dependent on the location and distance away from the source object.
2.2 Sound Power and Heater Power
The heater generates a particular amount of heat per hour. The power required to generate this heat is the same, no matter what the temperature in the room. The heater power is measured in energy over time, or Watts. Sound power operates on the same principal – the sound power of an object is solely a property of the object, and is independent of the sound pressure levels in the room. Sound power is the rate at which sound energy is emitted per unit time. Sound power is also measured in Watts.
2.3 Sound Intensity and Heat Flow
Heat travels and flows throughout the room. The heat flow has a temperature level and a direction. Sound intensity is the measure of the flow of sound, and has a level and a direction. This flow is observed over a specific area, hence the units of sound intensity are W/m2.
*** In this analogy, it was assumed that both the heater and sound emitting object have a constant output. The room was assumed to be free of reflections and other sources. ***
3. Relationship of Sound Pressure, Sound Power and Sound Intensity
Sound pressure, sound power, and sound intensity can be related to each other under some specific circumstances.
3.1 Sound Pressure and Sound Intensity Relationship
In an acoustic free field, the sound intensity is directly related to sound pressure by the following equation:
Sound Intensity = (Sound Pressure) x (Particle Velocity)
The particle velocity is the speed of which the air molecules vibrate back and forth while transmitting a sound. Particle velocity is a vector quantity, while sound pressure is only a scalar amplitude. The result is that sound intensity is a vector quantity.
At any given location around a sound source, either the sound intensity or sound pressure can be measured, as shown in Figure 3.
Figure 3: Sound Intensity (left) versus Sound Pressure (right) around an electric motor
The sound intensity (left side) shows both amplitude (via color) and direction (with a vector arrow). The sound pressure (right side) shows only amplitude with color:
Amplitudes the Same - Looking at the color distribution of sound intensity and sound pressure amplitude levels, the same pattern is present in both images.
Direction is the Difference - The sound intensity vectors on the left side of Figure 3 clearly indicate the direction of sound flow, making it easier to troubleshoot the cause of the high sound levels. The sound pressure values on the right side do not indicate flow direction, or provide clues as to where the sound originated.
Sound pressure level can be measured with a single microphone, while sound intensity is a more complicated measurement. A sound intensity measurement requires two or more microphones in a specific arrangement. For example, the Simcenter Soundbrush uses four microphones in a tetrahedral pattern to measure intensity.
3.2 Sound Intensity and Sound Power Relationship
It is easy to convert from sound intensity to sound power (and vice versa), if the area over which the measurement was performed is known:
Sound intensity is expressed in Watts/m2.
Sound power is expressed in Watts.
Multiply the sound intensity value by the area (in m2) covered by the measurement to calculate sound power.
In an acoustic free field, the sound intensity at a specific distance from a sound emitting object can be calculated, if the sound power of the object is known. Take a printer that has a sound power of 0.02 Watts. Sound intensity will be measured in a 2 meter hemi-sphere around the printer as shown in Figure 4.
Figure 4: Object with known sound power in 2 meter hemi-sphere test
To get the sound intensity, divide the sound power by the area of the hemi-sphere:
Sound power is 0.02 Watts
Hemi-sphere surface area is 25 m2 (2 meter radius)
Sound intensity is 0.02W/25m2 for a value of 0.0008 W/m2
Equation 1: Conversion of power measured quantities to decibels
Using the following values in Equation 1:
Reference value for intensity (1x10-12 W/m2 from Figure 1) for Wref
Sound intensity of 0.0008 W/m2 for W
The sound intensity at two meters distance is 89 decibels.
Sound pressure, sound power, and sound intensity are acoustic quantities that can be expressed in decibels. They describe different aspects of sound, and the decibels for each represent different measurement quantities.
Sound Pressure – Indicates the amplitude level of sound at a specific location in space, and is a scalar quantity. The level is dependent on the location and distance the sound is observed relative to a sound source. Sound pressure is measured in Pascals.
Sound Power – The rate at which sound is emitted from an object, independent of location or distance that the sound is observed. Sound power measurements are often specified in the noise regulations of many different kinds of products, from construction equipment to computer printers. Sound power is measured in Watts.
Sound Intensity – Sound intensity is sound power per unit of area. It indicates the flow of sound through a specific area. Sound intensity is measured in Watts/m2.