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Sound Absorption

Siemens Experimenter Siemens Experimenter
Siemens Experimenter

Sound Absorption

 

When sound reaches a barrier, three things can happen as shown in Figure 1:

  • Absorption – The sound is absorbed and dissipated as heat.
  • Transmission – Sound can pass through the barrier.
  • Reflection – Sound can be reflected back off the barrier.Figure 1: Sound at a barrier can be absorbed, transmitted, or reflected.Figure 1: Sound at a barrier can be absorbed, transmitted, or reflected.

The amount of absorption, reflection, and transmission of the sound is different for every frequency.

 

For example, a high frequency sound with a short wavelength can be absorbed by a thinner piece of material, while lower frequency sounds are not absorbed, due to their longer wavelength.

 

This article will explore what variables can effect sound absorption and how absorption can be measured.

 

Absorption Quantification

 

Absorption is can be expressed via the “absorption coefficient” (Equation 1) which can have a value between 0 and 1.

 

Equation 1: Calculating the absorption coefficient.Equation 1: Calculating the absorption coefficient.

Alpha represents the absorption coefficient.

  • When the absorption coefficient equals one, all the sound is absorbed
  • When the absorption coefficient equals zero, no sound is absorbed

Typically, the absorption coefficient for a given material is plotted as a function of frequency as shown in Figure 2.

 

Figure 2: Absorption curve.Figure 2: Absorption curve.

Between 50 and 100 Hz in Figure 2, 100% of sound is absorbed. Below 50Hz, the material does not absorb well. Thicker material may aid in helping to absorb the lower frequencies.

 

Some absorption values for different materials are below. All values are approximate. 

 

Figure 3: Absorption values.Figure 3: Absorption values.

 

Note that the softer the material, the more absorption. The more dense and hard the material, the less absorption.

 

What affects the absorption of a material?

 

There are several things that affect absorption. Some factors include: material composition, humidity, material thickness, and material position.

 

Material Composition

 

Porous materials typically absorb sound better than very dense materials. Examples of porous materials include cloth, foam, fiber glass, and acoustic tiles.

 

Porous materials present a larger amount of surface area to the advancing sound waves. The fibers or particles of the porous material are able to vibrate and dissipate the sound as heat.

 

Very dense materials (concrete, cinder block, glass) tend to reflect most of the incident sound.

 

Humidity

 

The speed of sound is affected by the humidity in the air.  The speed of sound increases as humidity increases. As the speed of sound increases, the absorption also increases, as shown in Figure 4.

 

 Figure 4: Effect of humidity.Figure 4: Effect of humidity.

When performing an absorption test, samples should be stored for several days in a humidity controlled room to ensure they are at the desired humidity for the test.

 

Material Thickness

 

With all else being equal, increasing material thickness increases the absorption performance at lower frequencies (Figure 5). It has been experimentally determined that peak absorption of a frequency occurs when the material thickness is about one-quarter the wavelength of the wave.

 

Figure 5: Absorption performance versus material thickness.Figure 5: Absorption performance versus material thickness.

 

Low frequency sounds have longer wavelengths, therefore the material has to be thicker to absorb lower frequency sounds.

 

Material Position

 

Sound absorption depends on angle of incidence ( ) of the incoming plane wave. Often, an “angle-averaged” value of absorption is used for design purposes.

 

Figure 6: The angle of incidence of the incoming plane wave.Figure 6: The angle of incidence of the incoming plane wave.

In addition to the angle of incidence, material position relative to the supporting wall matters.
For example, mounting the absorptive material flush with the wall versus mounting the absorptive material and leaving an air-gap between the material and the wall will affect the absorption coefficient. 

 

Figure 7: The effect of air between absorptive sample and reflective wall.Figure 7: The effect of air between absorptive sample and reflective wall.

Experimental data shows that leaving one quarter of a wavelength between the wall and the absorptive sample maximizes absorption at a given frequency.

 

This is because there is an inverse relationship between the pressure of the sound wave and the air molecule velocity.

 

As the wave hits a wall, the molecule velocity slows down because the wall resists the motion of the air molecules. At the wall, there is a high pressure, low velocity location.

  • The high pressure, low velocity location is called a node.
  • The low pressure, high velocity location is called an anti-node.

In the areas of low pressure, the molecules are less densely spaced. Therefore in the low pressure areas, the molecules can move more freely and at higher velocities. 

 

Figure 8: The inverse relationship between pressure and molecular velocity. In areas where the pressure is high, the molecular velocity is low. In areas where pressure is low, molecular velocity is high.Figure 8: The inverse relationship between pressure and molecular velocity. In areas where the pressure is high, the molecular velocity is low. In areas where pressure is low, molecular velocity is high.

Sound is absorbed when there is friction between the air molecules and the absorptive material causing the sound energy to dissipate as heat.

  • The higher the velocity of the air molecules, the more friction and the more absorption.
  • The lower the velocity of the air molecules, the less friction and the less absorption.

Looking at the graphic, you can see that the area of low pressure, high velocity, is one quarter wavelength away from the wall. Therefore, the absorptive material should be placed one quarter wavelength away from the wall to maximize the absorption of the wave.

 

Figure 9: Absorptive material (pink) is placed one quarter wavelength away from the wall to maximize absorption.Figure 9: Absorptive material (pink) is placed one quarter wavelength away from the wall to maximize absorption.

The concept of placing the absorptive material one quarter wavelength away from a wall is sometimes referred to as the “Quarter Wavelength Rule”.

 

Note that placing the material one quarter wavelength away from the wall maximizes absorption for that corresponding frequency. If it is desired to absorb a broadband range of frequencies, a thick piece of material must be used so that there is material “one quarter wavelength” away from the wall at many frequencies. There is a trade-off between material cost and the range of frequencies targeted with the “quarter wavelength rule”.

 

Measuring Absorption

 

There are two methods to measure a material’s absorptive properties: the tube method and the room method.

  • The tube method uses direct incidence. In this case, the sound waves all approach the sample at the same angle. See Figure 10.
  • The room method uses random incidence. In this case, the sound waves approach the sample at random angles. See Figure 10.

 Figure 10: The blue arrows represent sound waves. Direct incidence: all sound waves approach sample at same angle. Random incidence: sound waves approach the sample at random angles.Figure 10: The blue arrows represent sound waves. Direct incidence: all sound waves approach sample at same angle. Random incidence: sound waves approach the sample at random angles.

Measuring Absorption with an Impedance Tube: Direct Incidence

 

Hardware

 

Measuring a material’s absorption can be done with an “impedance tube”. These tubes are typically made of straight “sound proof” tubing (typically thick steel).

 

One end of the tube is connected to a sound source which outputs a broadband range of sound waves. The other end of the tube holds the sample to be tested. Therefore, the sound waves approaching the sample are both direct incidence and normal to the sample.

 

The tube ends in a rigid termination. A pair of microphones are positioned just before the sample.  See Figure 11 below.

 

 Figure 11: Top: Impedance tube. Bottom: cross section of the impedance tube to show sample location within the tube.Figure 11: Top: Impedance tube. Bottom: cross section of the impedance tube to show sample location within the tube.

 

Sample Preparation

 

Samples of the test specimen must be cut to fit within the tube. Care must be taken when cutting the samples as the boundary conditions between the sample and the tube can greatly affect the resulting measurements.

 

Some impedance tubes come with sample cutters that are designed to cut samples to the exact diameter of the tube. But, these material cutters can slightly compress the sample during cutting, altering the samples absorption properties.

 

Figure 12: Material cutter and some cut samples.Figure 12: Material cutter and some cut samples.

A better alternative to a sample cutter is using a waterjet to cut the material. A CNC waterjet will produce an accurately cut, repeatable sample. 

 

A well cut sample will fit flush with the tube and will neither compress nor leave a gap between the tube and the sample diameter.

 

Figure 13: Example of a well cut sample.Figure 13: Example of a well cut sample.

An improperly cut sample could be cut too large and compress when placed in the tube or be cut too small and leave a gap between the sample and the tube wall.

 

Figure 14: Two examples of improperly cut samples.Figure 14: Two examples of improperly cut samples.

 

In the above figure, the first sample was cut too large: the edges of the sample are compressed in the tube. The second sample was cut with too small: there is a gap between the tube and the sample.

 

Test

 

To test the absorption of the sample, a broadband signal is output by the speaker. Multiple averages are taken to ensure that random noise on the measurement is averaged out.

 

The result of the measurement is a graph of the absorption coefficient vs. frequency. See Figure 15 below.

 

Figure 15: The result of an absorption test in tube is the absorption coefficient of the material vs. frequency (bottom graph).Figure 15: The result of an absorption test in tube is the absorption coefficient of the material vs. frequency (bottom graph).

The above figure is taken from the LMS Test.Lab Absorption Testing using Impedance Tube software.

 

Measuring Absorption with a Reverberation Room: Random Incidence

 

It is not always practical to test a material’s absorption in an impedance tube. The impedance tube only tests a material’s absorption in a direct field (Figure 10). This does not accurately represent real world situations in which the sound is often random incidence (Figure 10). This is where testing using a reverberation room is valuable.

 

A reverberation room is designed to have hard, reflective walls built at oblique angles so no walls are parallel to each other.  This causes the sound waves to be reflected a maximum number of times around the room to help create a diffuse field.

 

Figure 16: Reverberation room are built with walls at oblique angles.Figure 16: Reverberation room are built with walls at oblique angles.

Often, hemi-spherical features are added to large walls to increase wave diffraction (spreading out), adding to the diffusivity of the chamber.  One of these hemispheres can be seen in Figure 17. 

 

Figure 17: Hemispheres are added to increase wave diffraction.Figure 17: Hemispheres are added to increase wave diffraction.

Common items to test using the reverberation room method are material samples (usually about 1m x 1m), acoustic panels, and even furniture.

 

The test requires two measurement conditions: 

  • Step 1: Measuring the reverberation time in the room with no test sample
  • Step 2: Measuring the reverberation time in the room with the test sample

It is recommended to take multiple measurements for each test condition and average the results to remove the effects of uncorrelated noise on the measurement.

 

Step 1: Characterize the absorption of the empty reverberation room

 

The first step is to characterize the reverberation room.

 

We need to test the room with and without the sample. The difference in reverberation time between the two conditions gives an indication of the absorption of the sample.

 

The absorption value is closely related to the reverberation time. See ISO 354:2003 for the exact equations and specs.

 

To determine the reverberation time of the room, a T60 decay time is used. This is the time in seconds it takes for the sound pressure level (SPL) to decrease by 60dB after the sound source is stopped.

 

The sound source is played for a number of seconds, then stops. After there is 5dB of attenuation, the decay time measurement starts (green dot in Figure 18). After 60dB of additional attenuation, the decay time measurement stops (red dot in Figure 18).

 

Figure 18: T60 decay time.Figure 18: T60 decay time.

It’s important to note that it is not always to possible to play a sound loud enough to get 60 dB of attenuation. Therefore T20 or T30 decay times are often used. These work the same way at the T60 decay time except they only require 20 dB or 30 dB of attenuation respectively. Even though the decay is only measured over 20 dB or 30 dB of attenuation, the decay times are projected for a 60 dB decay.  So even if the T20 or T30 methods are used, times are still reported as T60.

 

Figure 19: In LMS Test.Lab, it is possible to calculate the T20, T30, and T60 reverberation times in the Online Processing workbook.Figure 19: In LMS Test.Lab, it is possible to calculate the T20, T30, and T60 reverberation times in the Online Processing workbook.

Of course, the decay time can change with frequency, and is therefore measured for each octave band (see Figure 20).

 

Figure 20: The decay time is plotted for each octave band. This graph shows the decay time per octave band.Figure 20: The decay time is plotted for each octave band. This graph shows the decay time per octave band.

The reverberation time is closely related to the absorption of the empty room. After calculating reverberation time for each octave band, the absorption of the empty room is then calculated for each octave band.

 

Step 2: Characterize the absorption of the test sample

 

After characterizing the room, we now need to characterize the material sample.

 

A common test sample is a large material sample (typically about 1 meter x 1 meter).

 

Figure 21: Setup to measure absorption of a material sample (purple). Multiple microphones (grey circles) and sources (red boxes) are used in the reverberant room.Figure 21: Setup to measure absorption of a material sample (purple). Multiple microphones (grey circles) and sources (red boxes) are used in the reverberant room.

Now the reverberation time of the room with the sample in it is calculated.  

 

The reverberation time of the room with the sample should be shorter than the reverberation time of the room without the sample. This is because we expect the sample to add absorption to the room.

 

After calculating reverberation time for each octave band, the absorption of the empty room is then calculated for each octave band.

 

Steps 1 and 2 are now completed:

  • Step 1: Measuring the reverberation time in the room with no test sample. Calculate absorption of empty room.
  • Step 2: Measuring the reverberation time in the room with the test sample. Calculate absorption of room with sample.

To determine the absorption of just the test sample, the absorption of empty room is subtracted from the absorption of the room and sample.

 

Equation 2: the absorption of the sample is calculated by subtracting the absorption of the empty room from the absorption of the room with the sample in it.Equation 2: the absorption of the sample is calculated by subtracting the absorption of the empty room from the absorption of the room with the sample in it.

When testing an absorber in a reverberant room, the results of the test is the absorption coefficient with respect to frequency.

 

Figure 22: The calculated absorption coefficient vs. frequency (bottom right).Figure 22: The calculated absorption coefficient vs. frequency (bottom right).

The above is a screenshot of LMS Test.Lab Sound Absorption in Room Software.

 

Conclusion:

 

There are two common methods to measure sound absorption: in an impedance tube and in a reverberant room. Measuring in an impedance tube results in the absorption coefficient vs. frequency. Measuring in a reverberant room results in the absorption coefficient vs. frequency or the equivalent absorption area of the test sample vs. frequency.

 

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