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Sound Power and Sound Pressure

"Sound power" and "sound pressure" are two distinct and commonly confused characteristics of sound. Both share the same unit of measure, the decibel (dB), and the term "sound level" is commonly substituted for each. However, to understand how to measure and specify sound, the Motor system designer must first understand the difference between these properties. 

To obtain the maximum benefit from sound power level (Lw) ratings, an engineer must understand what Lw ratings represent and how to apply them properly. For the design engineer who is not yet familiar with the techniques of applying Lw ratings, this article may serve as a brief introduction.

Sound Power Ratings

Sound power is the acoustical energy emitted by the sound source, and is an absolute value. It is not affected by the environment.

Motor Lw ratings are obtained from the determination of sound power levels generated by a motor when it is operated at no load. These sound power levels are obtained in accordance with IEEE 85. What is heard is a sound pressure level that is determined, for any particular location, by many factors, including size of the room, nature of its walls, ceilings, furnishings, etc. The pressure level at the point of hearing is also related to the distance from the sound source. The motor is the starting point, and when proper and accurate consideration is given to the other components of the system, sound power level ratings in octave bands will allow calculation of the resulting sound pressure levels in the space. 

Sound power levels are connected to the sound source and independent of distance. Sound powers are indicated in decibel.

Lw = 10 log (W / W0)                   where:

W0 = reference power    (W)            

The normal reference level is 10-12 W, which is the lowest sound persons of excellent hearing can discern.   Sound power is measured as the total sound power emitted by a source in all directions in watts (joules / second).

Sound Pressure Level

Sound pressure is a pressure disturbance in the atmosphere whose intensity is influenced not only by the strength of the source, but also by the surroundings and the distance from the source to the receiver. Sound pressure is what our ears hear, what sound meters measure ... and what ultimately determines whether a design achieves quality sound. 

The sound pressure level in a space may be estimated when sufficient information is available from the Lw of motor and the acoustical characteristics of the space. A proper acoustical calculation requires the use of the motor Lw stated separately for each of the eight octave bands. Each octave band level is usually different, and the room acoustical characteristics also vary with frequency.

Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level.  Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors.

Sound Pressure Level (SPL)  $= 20 \log \frac{p}{p_{0}} = 10 \log (\frac{p}{p_{0}})^{2}$, where  po = 2x10-5 N/m2.

p = root mean square pressure  (N/m2)

The usual reference level po is 20x10-6 N/m2.  Note that the noise from motors is documented in sound power level.  "Threshold of audibility'' or the minimum pressure fluctuation detected by the ear is less than 10-9 of atmospheric pressure or about  20x10-5 N/m2 at 1000 Hz. "Threshold of pain'' corresponds to a pressure 106 times greater, but still less than 1/1000 of atmospheric pressure.  Because of the wide range, sound pressure measurements are made on a logarithmic scale (decibel scale).

Relating Power To Pressure

Equipment sound power ratings are determined in an acoustics laboratory, usually by the manufacturer. Specific standards qualify testing facilities and methods to promote data uniformity and objective comparisons of different units across the industry.

By contrast, sound pressure can be measured in an existing space with a sound meter, or predicted for a space not yet constructed by means of an acoustical analysis. Since the only accurate sound data a manufacturer can provide is expressed as sound power, the challenge of designing for quality sound is to examine the effect of environmental factors.

An Illuminating Analogy

The following comparison of sound and light may help illustrate the distinction between these terms. Think of sound power as the wattage rating of a light bulb; both measure a fixed amount of energy. Sound pressure corresponds to the brightness in a particular part of the room; both can be measured with a meter and the immediate surroundings influence the magnitude of each. In the case of light, brightness is more than a matter of bulb wattage.  Asking for a 90 dBA motor is a lot like asking for a “light:” you don’t know what you are going to get. Most of us are much more familiar with light than sound. If someone says he has a 100-watt light bulb, you have some idea of the candlepower available, but if you want to read by the light, you want to know the light intensity level at the reading location. To determine the light intensity level you would need to know:

  • “How far away is the light?” If the light is a mile away, it is not much use. The analogous sound question is “How far away is the motor?”

  • “Is the light outdoors?” With no walls to reflect the light, all but the direct light radiates out into the free field of space. The analogous sound question is “Is the motor outdoors?”

  • “Are the room walls reflective if the light is not outdoors?” A room covered with black velvet would not reflect much light regardless of its size. The analogous sound question is “How reverberant are the walls?”

Motor dBA Rating

The term dBA applies to sound pressure. The sound pressure immediately around a motor depends on a number of variables. Sound pressure can only be calculated from the motor sound power rating when using known variables. Motor manufacturers indicate the noise level of their products by sound pressure levels expressed in dBA. These figures refer to the sound pressure levels that should be experienced by an observer at a certain distance from the motor in a given environment, which is generally assumed to be a free field. These values should only be used to compare noise levels of similar types of motors at the same distance, and in the same environment.  Do not assume that the dBA levels on the performance data will in any way be similar to those achieved in practice.  Depending on circumstances, they can be substantially exceeded.

Sound Power to Pressure Conversion Rule of Thumb

 TYPICAL FREE FIELD SOUND PRESSURE
VERSUS SOUND POWER LEVELS - IN dB
 

FRAME SERIES

POWER LEVEL

PRESSURE LEVEL @ 3 FT

PRESSURE LEVEL @ 5 FT

140

X

X - 7.8

X - 10.6

180

X

X - 8.0

X - 10.8

210

X

X - 8.2

X - 10.9

250

X

X - 8.4

X - 11.1

280

X

X - 8.8

X - 11.4

320

X

X - 9.0

X - 11.6

360

X

X - 9.2

X - 11.8

400

X

X - 9.5

X - 12.0

440

X

X - 10.9

X - 12.4

5000

X

X - 10.6

X - 12.8

5800

X

X - 11.6

X - 13.7

6800

X

X - 11.9

X - 13.9

8000

X

X - 12.5

X - 14.7

  

Calculating Sound Pressure 

Sound instruments measure only sound pressure; this pressure varies depending on the surroundings. To calculate sound pressure from sound power, one must consider all the variables that affect sound pressure. The relationship between sound power level (sound energy emitted by the motor and sound pressure (what is heard) at a specific location.

Human Response

Ear sensitivity varies with frequency. A low frequency sound at a certain power does not seem as loud as a higher frequency sound of the identical power. To account for this difference, a weighting scale has been developed. Sound power levels adjusted by this specific weighting scale are called A-weighted. Sound power levels in eight octave bands are calculated to a single A-weighted sound power number, LWA.

Free Field Ratings

Because one environment, a free field, can be easily defined, it is sometimes used to specify desired sound pressure levels. If a motor is placed on the ground in a large open field, all of its sound radiates out in a hemispherical free field with no sound reflected back. These conditions are fully defined, and it is possible to convert motor sound power to sound pressure at a specified distance. As distance from the motor increases, sound pressure decreases; so it is important to include distance from the motor when asking for a dBA rating.  If you specify a hemispherical free field but do not specify a distance, it is possible to make a loud motor appear quieter by calculating its sound pressure level at a distance farther away from the motor. For example, Motor A calculates to 90 dBA at a distance of 3 m (10 ft) in a hemispherical free field. Another motor, Motor B, with a sound power level 12 dB higher than Motor A, will also calculate to 90 dBA, but at 12 m (40 ft) from the motor!

Multiple Sources

Two equal sources produce a 3 dB increase in sound power level.  Two equal sources produce a 3 dB increase in sound pressure level, assuming no interference.  Two 80 dB sources add to produce an 83 dB SPL.