Sound Power, W 

Sound power is another physical parameter of sound related to the rate of acoustic energy output  from a sound source. The unit of sound power is watt (W). Sound power is the total energy generation rate of a sound source, therefore the sound power of a sound source is not affected by the environment and remains a constant.

For example, a  higher power sound source always generated a high sound pressure than a lower power sound source at a given point of an environment. However, the sound pressure generated by a higher sound source may varies with location, time and environment. Some sound level measurement may even lower than that generated by the lower power sound source because teh acoustic pressure are highly depends on the surrounding environment.

So, Sound power is a measurement of the flow rate of acoustic energy and is independent from any point in space or time.

In general, the acoustic energy of a sound source passing through a small surface element as a given radius decreases as the distance increase. However, the integration of the energy of over the whole surface remains constant.

Although both sound pressure and sound power depends on the sound source. The reading of sound pressure also depends on the position of the receiver and are highly affected by the environment, such as shape and dimension of environment, interference with other sound sources etc. While the reading of sound power measures the sound source of an enclosed measuring surface and is not sensitive to the noise source outside the measuring surface. Therefore the sound pressure measurement can be used to measure the response of receiver and the sound power measurement can be used to identify the sound source of a noise. Besides, the measuring of sound pressure is much easier than the measuring of sound power.  

Sound Power Level

Similar to sound pressure, the range of sound power is also very wide, algorithmic scale is also defined. And a reference power of 10^-12 is used. The sound power level is defined as:

where

L_W is the sound pressure level
W is the sound power (W)
W_o is the reference sound power, 10^-12watts (W)

The sound power of a sound source in term of sound power level is:

Sound Intensity, I

Sound intensity is defined as the sound power passing through a unit area.

where

I is sound intensity of source, W/m²
W is sound power of a source, W
A is surface area, m²

Sound intensity is not a property of sound source. But it is an important linkage between sound power and the measurable sound pressure.

For example, the average sound intensity of a free propagating plane wave can be expressed as the sound pressure as follows:

.

where

I is sound intensity of source, W/m²
P_rms is rms sound pressure
ρc is density of the medium
c is speed of sound in the medium

Sound Intensity Level

Similarly, the range of sound power is also very wide, algorithmic scale is also defined. And a reference intensity of 10^-12 is used. The sound intensity level is defined as:

.

where

L_I is sound intensity level
I is sound intensity, W/m²
I_o is the reference intensity, 10^-12W/m²

With the reference intensity equals to 10^-12W/m², the sound intensity level, L_I and the sound pressure level, L_p are numerically equal, that is L_I=L_p.