What is Sound Power?

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Sound Power

 

How to measure how much sound a object produces? 

 

This article describes how to measure the sound power of a object.  It has the following sections:

 

   1. Measurement Considerations and Background

   2. Sound Power: Pressures versus Surface Area

   3. Correction Factors

        3.1 Background Correction: K1

        3.2 Reflections: K2

   4. Conclusions

 

To understand how a sound power measurement works, it is helpful to understand the difficulties of measuring sound with a single microphone.

 

1.  Measurement Considerations and Background

 

Consider the speakers in Picture 1. For the purposes of this article, assume that the speakers are producing a constant, steady state noise that does not vary over time.

 

speaker_how_loud.pngPicture 1: Speakers making sound

Can the sound level be determined by placing a microphone nearby (Picture 2), and measuring the decibel level? Unfortunately, this is not the case.

 

speaker_how_loud_mic.pngPicture 2: Measuring speaker sound with microphone

Where to place the microphone?  How far away?  The further distance a microphone is away from a sound emitting object, the lower the decibel value will be (Picture 3)Distance certainly affects the sound level.  Instead of a single value, the level changes depending where the measurement is taken.

 

speaker_how_loud_distance.pngPicture3: Sound measurement microphones located 1 meter and 2 meters away from speakers

In an acoustic free field, the sound pressure level drops by 6 dB when doubling the distance away from the sound emitting object.  Measuring from 2 meters versus 1 meter away would decrease the sound level by 6 dB.  If a product had a requirement to be below 50 dB, but the microphone distance was not specified, the microphone could just be placed far enough away to meet the requirement!

 

Even if a microphones were placed at a consistent distance away, the decibel reading could vary depending on the location relative to the object, as shown in Picture 4

 

speaker_how_loud_location.pngPicture 4: Sound measurement microphones at the same distance from sound emitting object, but at different distances.

In Picture 4, the microphone placed behind the speakers will not read the same decibel level as a microphone placed in front of the speakers.  The levels are different, even though the distance away from the speakers is the same.

 

How to measure the sound of an object independently of the distance or location of the microphone?  The answer is sound power.

 

Sound power attempts to quantify the acoustic source strength of an object, independent of the distance and location of the measurement.

 

sound_power_key1.png

 

How is sound power measured in practice?

 

2. Sound Power: Pressures versus Surface Area

 

There are different methods used to quantify the sound power of an object.  A common method is to surround the object with multiple sound pressure microphones (Picture 5). 

 

hemi_sphere.pngPicture 5: Hemi-sphere arrangement of microphones around test object, above a reflecting plane. Left: Drawing with red dots representing microphone locations. Right: Actual sound power test system.

For example, the microphones might be placed around the object in hemi-sphere, to capture all the sound emitted by the object in all directions. By taking an energy average of the microphone pressures, the result is a measurement of sound that is independent of location. See the “Sound Pressure” portion of Equation 1

 

To normalize the microphone readings over distance, the surface area of the hemisphere is calculated and then converted into decibels. See the “Surface Area” portion of Equation 1. By calculating the surface area of the hemi-sphere, the measurements are made independent of the distance.

 

equation1.pngEquation 1: Sound power based on Surface Area and Sound Pressure

Equation 1 is the basic formula for Sound Power (Lw), where L is the sound level and w stands for watts (the units in which sound power is reported):

  • Lp is the a sound pressure spectrum.  It is measured in octave format with A-weighting applied. L is short for Level (sum of the octave values), and p is for pressure.
  • N is the number of microphone locations on the surface area for the measurements.
  • S is the surface area that the microphones are arranged over for the sound power measurement.
  • So is a reference surface area of 1 m2.
  • Lw is the output of the sound power measurement.  It is an A-weighted sound power spectrum (as shown in Picture 7) in octave format. L is short for level, and w is for watts.

Sound power is typically reported in decibels referenced to 1 PicoWatt (1 pW).

 

The equation has two major parts:

  • Sound Pressures - The sound pressure readings from the different microphones (Lp) are averaged together and converted into decibels
  • Surface Area – The surface area over which the microphones are arranged are converted to into decibels. The reference surface area (So) is 1 m2.

 

The sound power of an object is always be the same no matter what size hemisphere is used to measure the sound power. The pressures and surface area work in conjunction with each other to make the total sound power always be the same (Picture 6).

 

 

equal_sound_power.pngPicture 6: Cross section of hemi-sphere shaped sound power arrangement. Left shows microphones close to object which increases sound pressure readings, but has smaller surface area. Right shows larger surface area with microphones farther from object.

As the surface area gets smaller, the microphones are at a closer distance to the test object:

  • The closer the microphones are to the object, the higher the sound pressure readings.
  • The higher sound pressure readings are offset in the equation by the reduction in surface area.

So, the total sound power (Lw) remains the same!

 

Conversely, as the area increases, the microphones get farther from the test object.  The farther the microphones are from the test object, the lower their sound pressure readings.

 

The sound power equation is setup so that any changes in sound pressures are offset by equivalent changes in the surface area, so the total sound power remains constant.

 

sound_power_spectrum.pngPicture 7: Sound power spectrum test result – A-weighted decibels referenced to Watts versus octave bands

 

The final results of a sound power test would be a A-weighted octave spectrum (Picture 7).  It has units of decibels referenced to Watts.

 

sound_power_key2.png

 

 

3. Correction Factors

 

Sound power tests are run in a variety of facilities of differing quality and performance. Correction factors can be used to remove some of the variation found between test facilities.

 

The Sound Power equation that was presented in Equation 1 assumes that there is no other sound sources nearby. It also assumes that there are no reflective walls in close proximity to the test, other than the reflecting plane of the ground. In a virtual CAE sound simulation, this could easily be the case (Picture 8).  But in real-world practice, there can be reflections and other sound sources. 

 

virtual_sound_power.pngPicture 8: A virtual CAE simulation of a sound power test does not have extraneous background noises

The correction factors, K1 and K2, are used to remove the effects of reflections and other sources, within certain limits.  These corrections are performed on an octave band basis.

 

3.1 Background Correction:K1

 

When performing a sound power test, a measurement is made without the test object emitting noise.  This is called the background noise measurement.  This correction is done per octave band. Depending on the levels of the background noise compared to the actual test, a few corrective actions might be made:

 

  • If the background levels are higher than the noise emitting object under test, the entire test is not valid.
  • If the background levels are extremely low compared to the test object, no correction is made. This is the case for background levels 15 dB below or less than the measurement levels.
  • If the background noise is within a prescribed range compared to the actual test, the contributions of the background noise can be subtracted from the total sound power.

3.2 Reflections: K2

 

Some test environments are not perfectly anechoic.  Sound reflects back from areas other than the reflecting plane, causing the sound power levels to be higher than they should be. The amount of reflected noise can be quantified and corrected.

 

To do this, a reference sound source is measured in the test environment.  The reference sound source creates a repeatable, known sound power level.  For a given octave band, if the reference sound source should be 90 dB, but 91 dB is measured due to extra reflections, the increase can be corrected.

 

These two correction factors are subtracted from the sound power value. See Equation 2.

 

equation2.pngEquation 2: Sound Power equation with sound pressures, surface area, and correction factors

Where

  • Lp is the a sound pressure spectrum.  It is measured in octave format with A-weighting applied. L is short for Level (sum of the octave values), and p is for pressure.
  • N is the number of microphone locations on the surface area for the measurements.
  • S is the surface area that the microphones are arranged over for the sound power measurement.
  • So is a reference surface area of 1 m2.
  • Lw is the output of the sound power measurement.  It is an A-weighted sound power spectrum (as shown in Picture 7) in octave format. L is short for level, and w is for watts.
  • K1 is a correction for background noise
  • K2 is a correction for the environment or measurement room

 

With the addition of correction factors, the sound power equation is now complete.

 

sound_power_key3.png

 

 

4. Conclusion

 

Sound power attempts to quantify the acoustic source strength of an object, independent of the distance and location of the sound measurements.

 

mower_sound_power.pngPicture 9: Sound power test in progress with microphones in hemi-sphere arrangement

 

There are four main factors taken into consideration when calculating sound power (Equation 2):

 

  • Sound pressure measurements – An array of several microphones is used to measure sound pressures around the sound source test object. The density of the microphone arrangement is to make sure the level is measured correctly without any location dependency
  • Surface Area – The surface area used for the microphone arrangement is measured and used to compensate for the microphone distance from the sound source test object.
  • K1 Correction – Takes into account background noise of the test facility. Under certain circumstances, the calculated sound power can be corrected for the background noise
  • K2 Correction – Corrects for extra reflections that would make the calculated sound power higher than it should be.

 

Sound power is often used in noise regulations and legal certifications because it is not location or distance dependent. ISO 3744 and other standards have in-depth details on how these measurements are to be performed.

 

Questions?  Email peter.schaldenbrand@siemens.com.

 

Also be sure to check out the Fundamentals of Acoustics on-demand webinar.

 

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Comments
Enthusiast
Enthusiast

can I use a single microphone sensor to generate Hemisphere for sound power measurement?

Experimenter
Experimenter

Good article with clear and simplified explanation!:smileyhappy Smiley Happy

Siemens Phenom Siemens Phenom
Siemens Phenom

Hello Ravi,

 

I apologize for the late response, we just noticed your unanswered question.

 

I suppose a single measurement microphone could be used but it would require a lot of runs and you'd want each run to be very repeatable.  So, yes it's possible but I have not seen this done. To get sound power it would be 8-10 runs (for 8-10 microphones), and to use the K1, K2 corrections it would be another 16-20 runs.

 

With 8-10 microphones, it would be 1 run without corrections and 1-2 additional runs with the K1, K2 corrections.

 

Kevin