Simcenter Testing Solutions Sound Intensity

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Measuring sound?  While sound pressure indicates the amplitude, it is a scalar quantity only. Sound intensity (or acoustic intensity) is vector quantity which indicates the flow of acoustic energy. Sound intensity has both a magnitude and direction.
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Figure 1: Examples of sound intensity measurement results on a guitar while plucking one string (left) and a dryer (right). Sound intensity has both magnitude and direction.The direction is indicated by the arrow, while the magnitude of the sound is indicated by the color.

Sound intensity measurements:
  • Can be used to perform sound source localization
  • Can be used to calculate sound power
Due to the vector nature of sound intensity, the above measurements can be performed in-situ, (i.e., even in the presence of background noise).

This article contains the following sections:
  1. Definition
  2. How is Sound Intensity Measured?
  3. Spacer Length and Valid Frequency Range
  4. Probe Orientation and Amplitude Effects
  5. Scanning Techniques for Sound Power
  6. Calculating Sound Power from Sound Intensity
  7. In-Situ Measurements
  8. Measuring and Analyzing Sound Intensity
1. Definition

Sound intensity is the amount of sound energy radiated through a unit area.  It has units of Watts/m^2.

It is a vector quantity with both a magnitude and a direction (see the left side of Figure 2, below). The sound intensity graphic shows both the direction of the sound (indicated by the arrow) as well as the level (indicated by the color). This is different than sound pressure (Figure 2, right) which just shows the level (indicated by color). While sound pressure indicates the level of sound, it does not indicate the direction the sound is traveling.

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Figure 2: Sound intensity has both magnitude and direction (left) indicated by the arrow and color respectively. Sound pressure has a magnitude (right) indicated by the color.

Sound intensity is represented by vector quantity “I” and is calculated by multiplying the measured sound pressure level (scalar) by the particle velocity (vector). Particle velocity is the speed at which air molecules vibrate back and forth while transmitting a sound.
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Equation 1: Sound intensity is calculated by multiplying pressure by particle velocity.

Sound intensity is typically reported in decibels, with the reference value being 1x10^(-12) W/m^2.

2. How is Sound Intensity Measured?

There are two main types of sound intensity probes:
  • Pressure-velocity (PU) probes: one microphone, one particle velocity sensor
    • Advantage: sound intensity can be directly calculated using Equation 1 above, which is applicable over a wider frequency range
    • Disadvantage: PU probes are more fragile and more costly.
  • Pressure-pressure (PP) probe: two microphones separated by a spacer.
This article will focus on PP probes.

Pressure-pressure probes consist of two, phase-matched microphones that are positioned face-to-face and separated by a spacer.
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Figure 3: The sound intensity probe consists of two microphones. Two microphones are required to obtain the directional (vector) information.

Particle velocity can be determined using Equation 2, below. The pressure gradient between the two microphones is calculated based on the distance between the microphones (delta r, spacer distance) and the pressure value at each microphone. This can be integrated over time and divided by the density of the fluid medium (rho) to get an estimate for particle velocity (v). 
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Equation 2: Determining particle velocity based on pressure and spacer size.

The pressure component of Equation 1 is determined by taking an average of the pressure between the mics.
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Equation 3: Determining average pressure between the microphones on the intensity probe.

The two components of the equation come together to determine intensity using a pressure-pressure probe:
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Equation 4: Determining sound intensity using a pressure-pressure probe.

The above equation is for calculating sound intensity in the time domain.

As the above calculation takes the difference between the microphones, the microphones should be phase-matched.  Any difference in phase is interpreted as intensity. 

Phase-match refers to the comparison between the frequency response of two different microphones.  Ideally, when two microphones measure the same pressure wave, they should produce identical frequency, amplitude, and phase. There can be differences in the measured signals due to small differences in the construction of the microphones, which alter the response.  Because the measurements will not be identical, there is typically a specification.  For example, 0.3 degrees difference maximum over the entire frequency range.

3. Spacer Length and Valid Frequency Range

Note that Equation 4 is valid only for a certain frequency range.

The spacer between the microphones determines the frequency range for which intensity can be measured. Different spacer lengths are valid for calculating data over different frequency ranges.

The spacer distance determines the frequency limit (based on wavelength of sound):
  • The shorter the spacer, the higher in frequency the probe can measure
  • The longer the spacer, the lower in frequency the probe can measure
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Figure 4: The wider the spacer, the lower in frequency the probe can measure (and vise versa).

Note that the frequency ranges shown in this figure are to illustrate that the frequency range covered is dependent on the spacer distance. The frequency ranges shown are nominal values but can be adapted to actually represent what the intensity probe with the spacer corresponds to, I.e., as published by the probe manufacturer. This published range can be wider than the theoretical limits due to enhancements done by the probe manufacturer.

As a rule of thumb, the spacer length must be less than 1/6th the wavelength of interest in order to measure the pressure difference properly. If the spacer is larger than this, the pressure gradient estimation will become inaccurate and Equation 4 will no longer hold.

In Figure 5, below, a spacer is shown measuring two different wavelengths. On the left side of the figure (green), the spacer is an appropriate length to get a linear approximation of the change in pressure over change in distance of the sine wave for the lower frequency wave. On the right side of the figure (purple), the spacer is too wide to accurately measure the higher frequency wave.  The linear approximation fails.
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Figure 5: The spacer should be less than 1/6th the wavelength to ensure the linear approximation of change in pressure over the spacer distance holds.

Due to this, the intensity probe has a narrower valid frequency range than a single conventional microphone.

To cover a wide frequency range, it may be necessary to perform multiple measurements, with different spacer lengths. The data is then combined into one overall measurement covering the whole frequency range of interest. Simcenter Testlab supports measuring simultaneously multiple microphone probes with different spacer lengths.

4. Probe Orientation and Amplitude Effects

Directionality is critical when measuring with a sound intensity probe. The probe measures the pressure difference between two microphones. Therefore, the measurement is dependent in how the probe is oriented in the sound field.

If the probe is aligned with the sound field, the intensity probe will capture the maximum value of the intensity. The intensity probe should be oriented orthogonal to the measurement surface of interest (as shown in Figure 6, below).
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Figure 6: The intensity probe is aligned with the sound field. Therefore, the probe measures the maximum intensity.

If the probe is misaligned with the sound field, the intensity measurement will not capture the full measurement of the field.

Imagine the intensity probe is measuring the same sound field as above, but the probe’s orientation is changed. In this case, both microphones will measure the same pressure value at the same time. This makes the pressure difference zero in Equation 4 (pink portion) and thus forces the intensity value to zero.
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Figure 7: Because the microphones read the same pressure value, the probe measures an intensity of zero.  

If the intensity probe is oriented at an angle to the sound field, the probe will measure a value that is dependent on that angle.
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Figure 8: Here, the intensity probe will measure a lower intensity than if it was perfectly aligned with the sound field. The value is dependent on the angle, alpha.

Again, to properly measure a surface, the intensity probe should be oriented orthogonal to the surface so it is aligned with the sound field.

5. Scanning Techniques for Sound Power

To measure a sound source, an imaginary surface is built around that source (could be a hemisphere, cube, etc.). This surface is often referred to as a “mesh”.

Then, the intensity probe is roved over the surface to gather intensity values.

There are two main roving techniques: the discrete point method, and the scanning method (Figure 9, below).
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Figure 9: ISO 9614-1 Discrete point-by-point method versus ISO 9614-2 scanning methods.
  • Discrete point method: divide the surface into smaller areas, measure in one discrete location for a period of time
    • Advantage: results can be used for sound source localization as there will be discrete sound intensity points
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                     Figure 10: Sound intensity source localization result.
    • Disadvantage: longer time to scan
  • Scanning method: scan evenly over a surface for a period of time
    • Advantage: faster than discrete point method
    • Disadvantage: lacks detail the discrete point method provides, so it cannot be used for sound source localization
As an alternative to these scanning methods, it is possible to use the Simcenter Soundbrush, which is an intensity probe with an integrated 3D tracking system.
6. Calculating Sound Power from Sound Intensity

It is simple to convert between sound intensity and sound power, if the area over which the measurement was performed is known:
  • Sound intensity is expressed in Watts/m2
  • Sound power is expressed in Watts
Multiply the sound intensity value by the area covered by the measurement to calculate sound power.

Example: An air conditioning system is measured using the scanning method. It is determined that the sound intensity is 0.005 W/m2. The area that was measured was 2 m2.
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Figure 11: Converting between sound intensity and sound power.

Sound power is calculated by multiplying the intensity by the area. Therefore, the sound power equals 0.010W. This is equivalent to 100dB (the reference value for sound power is 1x10-12 W). 

7. In-Situ Measurements

An advantage of using a sound intensity probe to calculate sound power is that it is possible to perform in-situ measurements, as long as the background noise is steady state and constant thru the entire measurement process. This eliminates the need for expensive anechoic chambers.

Imagine performing a sound intensity scan on an engine while there is a vacuum running in the background. To complete the measurement, sound intensity must be measured on all sides of the box surrounding the engine.
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Figure 12: It is possible to perform intensity measurement even with background noise present.

The intensity value that the vacuum subtracts from the left side of the acoustic mesh will be compensated for as that same acoustic energy leaves the right side of the acoustic mesh. The net effect of the vacuum on the sound power calculation for the engine will be insignificant.

8. Measuring and Analyzing Sound Intensity

For information on how to measure sound intensity, check out this dedicated article.
For information on processing measured sound intensity, check out this dedicated article.

Questions?  Email or contact Siemens Support Center.

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KB Article ID# KB000044412_EN_US



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