# Relationship of sound pressure power and intensity

### Intensity – The Physics Hypertextbook

Pressure fluctuations caused by sound waves are much easier to measure. By definition, the intensity (I) of any wave is the time-averaged power (⟨P⟩) it transfers .. We get this thing again — the intensity-pressure amplitude relationship. If we wish to know the sound power transmitted the Sound Pressure Level of his fan for a particular duty. . noise intensity and quality in one single number. Intensity (I) is referred to as a "sound field quantity" as opposed to the "power field " relationship between a sound pressure (actually the rms of sound pressure.

Pressure, Power, and Intensity: A noise emitting object creates sound in a similar fashion.

### Acoustics Chapter One: What is Amplitude? | page 3

The following parallels can be drawn: Sound Pressure and Temperature At every position in the room, there is a specific temperature level, which is measured in degrees.

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. 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. 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.

• Introduction to Computer Music: Volume One

Sound Pressure and Sound Intensity Relationship In an acoustic free fieldthe sound intensity is directly related to sound pressure by the following equation: 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. 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. The period of a sound wave is typically measured in milliseconds. There are some optical techniques that make it possible to image the intense compressions are rarefactions associated with shock waves in air, but these are not the kinds of sounds we deal with in our everyday lives.

Pressure fluctuations caused by sound waves are much easier to measure. Animals including humans have been doing it for several hundred million years with devices called ears. Humans have also been doing it electromechanically for about a hundred years with devices called microphones. All types of amplitudes are equally valid for describing sound waves mathematically, but pressure amplitudes are the one we humans have the closest connection to.

## Sound intensity

In any case, the results of such measurements are rarely ever reported. Instead, amplitude measurements are almost always used as the raw data in some computation. When done by an electronic circuit like the circuits in a telephone that connect to a microphone the resulting value is called intensity.

When done by a neuronal circuit like the circuits in your brain that connect to your ears the resulting sensation is called loudness. The intensity of a sound wave is a combination of its rate and density of energy transfer. It is an objective quantity associated with a wave.

Loudness is a perceptual response to the physical property of intensity. It is a subjective quality associated with a wave and is a bit more complex. As a general rule the larger the amplitude, the greater the intensity, the louder the sound.