Simcenter Testing Solutions What is Sound Power?

Direct YouTube link: https://youtu.be/erZeRdcqYmg

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. Reflecting Planes
4. Correction Factors
     4.1 Background Correction: K1
     4.2 Reflections: K2
5. Sound Power Results
6. 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 Figure 1. For the purposes of this article, assume that the speakers are producing a constant, steady state noise that does not vary over time.

Figure 1: Speakers making sound.

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

Figure 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 (Figure3). Distance certainly affects the sound level. Instead of a single value, the level changes depending where the measurement is taken.

Figure 3: 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 Figure 4.

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

In Figure 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.

How is sound power measured in practice? This is covered in the next section.
 

2. Sound Power: Pressures versus Surface Area

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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 (Figure 5).

Figure 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.

Equation 1: Sound power based on Surface Area and Sound Pressure

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

• L_p 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.
• S_o 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 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 (L_p) 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 (S_o) 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 (Figure 6).
 

Figure 6: As the hemisphere size increases (and its corresponding surface area), the sound pressures decrease which makes the total

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 (L_w) 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.

3. Reflecting Planes

Depending on the product being tested, a reflecting plane might be used in the test.  Normally, a sound power test is performed in a facility that is treated with sound absorbing material.  The sound absorbing material prevents reflections that would increase the sound levels artificially.

A reflecting plane is a hard surface that does not absorb sound.  These are used in sound power tests to mimic real world conditions.  Tests can be performed with no reflecting planes, a single reflecting plane, or two reflecting planes as shown in Figure 7.
 

Figure 7: Left - A fully anechoic setup with no reflecting planes to measure sound emitting object (grey).  Middle - A single reflecting plane (blue) underneath under the test object (grey).  Right - Two reflecting planes (blue). The spherical grid represents where microphones are placed.

The number of planes is determined by how the object is utilized in real life.  For example:

• No Planes: Product like cell phones radiate sound in all directions while in use.
• One Reflecting Plane: Vehicles drive on hard road surfaces which are underneath them.  A single plane is used to represent the road surface.
• Two Reflecting Planes: White goods, like refrigerators and washers, usually have a reflecting plane underneath (the floor) and behind them (the wall).

The number of planes to be used would be defined in the sound power standards for a given product: Noise level certification, how to select the right standard?

4. 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 sound simulation, this could easily be the case (Figure 8). But in real-world practice, there can be reflections and other sound sources.

Figure 8: A virtual 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.

4.1 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.

4.2 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.

Equation 2: Sound Power equation with sound pressures, surface area, and correction factors

Where

• L_p 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.
• S_o 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.

5. Sound Power Results

The final results of a sound power test would be a A-weighted octave spectrum (Figure 9).

Figure 9: Sound power spectrum test result – A-weighted decibels referenced to Watts versus octave bands.

The graph is broken into octave bands on the frequency axis.  The amplitude is expressed in decibels referenced to the engineering unit Watts.

6. Conclusion

Sound power tests (Figure 10) attempt to quantify the acoustic source strength of an object, independent of the distance and location of the sound measurements.

Figure 10: 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.

More about sound power in these two articles:

• Sound Pressure, Sound Power, and Sound Intensity: What’s the difference?
• Noise level certification, how to select the right standard?

Questions? Email peter.schaldenbrand@siemens.com.

Related Links:

• Index of Testing Knowledge Articles
• History of Acoustics
• Microphone Basics
• Sound Pressure
• What is a decibel?
• What is A-weighting?
• Octaves and Human Hearing
• Decibel Math
• What is the Acoustic Quantity called Q?
• Sound Intensity
• Sound Absorption
• Sound Transmission Loss
• Noise level certification, how to select the right standard?
• Sound pressure, sound power, and sound intensity: What is the difference?
• Sound fields: Free and diffuse field, near and far field
• Loudness and Sones
• Calculating a Specific Loudness Spectrum in Simcenter Testlab
• How to Calculate N10 Time Varying Loudness in Simcenter Testlab?
• Articulation Index
• Auditory Masking
• Tone-to-Noise Ratio and Prominence Ratio
• Fluctuation Strength and Roughness
• Critical Bands in Human Hearing
• Simcenter Testlab Sound Diagnosis
• Simcenter Testlab Pass-by Noise Testing
• Sound Quality Jury Testing
• Describing Sounds with Words
• NVH Testing and Data Acquisition
• Fundamentals of Sound Seminar - Part I
• Fundamentals of Sound Seminar - Part II
• Acoustic Testing YouTube Playlist