Frequency-Dependent Sound Absorption

Abstract

Objective

The objective of this project is to determine if sound absorption by acoustic foam and similar materials changes with the frequency of sound.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on:

• Hoffman, M.K., 2003. "Sound Off: Frequency Dependent Sound Absorption," California State Science Fair Abstract [accessed October 3, 2006] http://www.usc.edu/CSSF/History/2003/Projects/J1515.pdf.

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Introduction

Sound Is a Wave

You will need to understand some basic properties of waves to get the most out of this project. We'll provide a quick introduction here, but for a more complete understanding we recommend some background research on your own. The Bibliography section, below, has some good starting points for researching this project.

What is sound? Sound is a wave, a pattern—simple or complex, depending on the particular sound in question—of changing air pressure. Sound is produced by vibrations of objects. The vibrations push and pull on air molecules. The pushes cause a local compression of the air (increase in pressure), and the pulls cause a local rarefaction of the air (decrease in pressure). Since the air molecules are already in constant motion, the compressions and rarefactions starting at the original source are rapidly transmitted through the air as an expanding wave. When you throw a stone into a still pond, you see a pattern of waves rippling out in circles on the surface of the water, centered about the place where the stone went in.

Sound waves travel through the air in a similar manner, but in all three dimensions. If you could see them, the pattern of sound waves from the stone hitting the water would resemble an expanding hemisphere. The sound waves from the stone also travel much faster than the rippling water waves from the stone (you hear the sound long before the ripples reach you). The exact speed depends on the number of air molecules and their intrinsic (existing) motion, which are reflected in the air pressure and temperature. At sea level (one atmosphere of pressure) and room temperature (20°C), the speed of sound is about 344 m/s.

You've seen that one way to describe a sound wave is by its speed. In addition to speed, we will also find it useful to describe sound waves by their frequency, period, and wavelength. Let's start with frequency (f). The top part of Figure 1, below, represents the compressions (darker areas) and rarefactions (lighter areas) of a pure-tone (i.e., single frequency) sound wave traveling in air (Henderson, 2004). If we were to measure the changes in pressure with a detector, and graph the results, we could see how the pressure changes over time, as shown in the bottom part of Figure 1. The peaks in the graph correspond to the compressions (increase in pressure) and the troughs in the graph correspond to the rarefactions (decrease in pressure).

Figure 1. Illustration of a sound wave as compression and rarefaction of air, and as a graph of pressure vs. time (Henderson, 2004).

Notice how the pressure rises and falls in a regular cycle. The frequency of a wave describes how many cycles of the wave occur per unit time. Frequency is measured in Hertz (Hz), which is the number of cycles per second. Figure 2, below, shows examples of sound waves of two different frequencies (Henderson, 2004).

Figure 2. Graphs of high (top) and low (bottom) frequency waves (Henderson, 2004).

Figure 2 also shows the period (T) of the wave, which is the time that elapses during a single cycle of the wave. The period is simply the reciprocal of the frequency (T = 1/f). For a sound wave, the frequency corresponds to the perception of the pitch of the sound. The higher the frequency, the higher the perceived pitch. On average, the frequency range for human hearing is from 20 Hz at the low end to 20,000 Hz at the high end.

The wavelength is the distance (in space) between corresponding points on a single cycle of a wave (e.g., the distance from one compression maximum (crest) to the next). The wavelength (λ), frequency (f), and speed (v) of a wave are related by a simple equation: v = fλ. So if we know any two of these variables (wavelength, frequency, speed), we can calculate the third.

How Does Sound Travel Through a Wall?

If sound is a pressure wave in air, how can sound pass through a wall? Let's think through how you can hear the sound of your neighbor's leaf blower when you're inside your house. The leaf blower creates a pressure wave (sound) in the air outside. This pressure wave hits the outside wall (and window) of your house, and causes each to vibrate. Let's consider the window first. If it is a single pane of glass, the vibration of the glass will cause the air inside the room to vibrate, creating a sound wave inside your room. Energy is lost at each of these transmission steps (and also as the distance from the sound source increases), so the sound inside your house is quieter than the sound outside. Another point is that the window will vibrate more easily at some frequencies than at others (this is a physical property of every material). Those "natural frequencies" of the window will be transmitted more efficiently, because it takes less energy to start the window vibrating at those frequencies.

In the case of the wall, there are more layers of material, meaning more transmission steps, and more loss of energy. The sound passing through the wall will be more attenuated than the sound passing through a single pane of glass.Another point is that the wall and the window, being made of different materials, probably have very different natural frequencies. The way each attenuates sound will be different for this reason too.

If your house has two rooms facing your neighbor's house, one with a window and without, listen to how the leaf blower sounds from each room. Which room is quieter? Does the pitch of the sound change at all? (This might be harder to hear.)

Decibels: How Sound Level Is Measured

The human auditory system is sensitive to a wide range of sounds, both in terms of frequency (pitch) and intensity (loudness). As we mentioned previously, a young person is typically able to hear frequencies ranging from 20 to 20,000 Hz. Humans can also detect sounds with intensities ranging over 13 orders of magnitude (powers of ten). In other words, the loudest sound a human can perceive is 10,000,000,000,000 times as loud as the softest sound that can be perceived!

When comparing sound intensities over such a wide range, it is inconvenient to keep lugging all of those zeros around, so units of decibels (dB) are commonly used instead. A decibel is defined as 10 × log(I ⁄ I_ref ), where I and I_ref  are the two intensities being compared.

So if I is 10 times louder than I_ref , that corresponds to an increase of:
10 × log(10 ⁄ 1) dB = 10 × 1 dB = 10 dB.

If I is 100 times louder than I_ref , that corresponds to an increase of:
10 × log(100 ⁄ 1) dB = 10 × 2 dB = 20 dB.

If I is 1000 times louder than I_ref , that corresponds to an increase of:
10 × log(1000 ⁄ 1) dB = 10 × 3 dB = 30 dB. And so on.

So you can see that for each power of ten change in intensity, there is a decade change (±10) in terms of dB.

Another useful dB fact to remember is that a two-fold change in intensity corresponds to ±3 dB. You can see this by plugging in 0.5 or 2 for the ratio I/I_ref in the definition for dB, above. When the measured level is half of the reference level, that's equal to -3 dB. When the measured level is twice the reference level, that's equal to +3 dB.

Decibels define a relative measure of sound intensity. In other words, it tells you how much louder or softer one sound is than another. However, if we choose a fixed point for the reference intensity level, then we have an absolute measure of sound intensity. A reference level that is often used in human auditory science is Sound Pressure Level (SPL), the lower limit of human hearing. SPL is defined as 10^-12 W/m², and is given a value of 0 dB (SPL). The recommended sound level meter for this project is calibrated in dB (SPL).

How Can You Block Sound?

The point of this project is to test different materials for their ability to block sounds of different frequencies. You should do background research on sound, sound-blocking materials, and sound-blocking construction techniques. Then come up with your own hypothesis about which materials might be better at attenuating low frequencies, and which materials might be better at attenuating high frequencies.

In order to test your hypothesis, you will need to obtain pieces of each of the different materials you want to test. You'll also need an audio test CD and a sound level meter. The audio test CD will have a series of pure tones at low, medium, and high frequencies. You will use these different tones and the sound level meter to test how well the different materials attenuate different frequencies.

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

• frequency,
• period,
• wavelength,
• amplitude,
• decibel,
• attenuation,
• soundproofing techniques,
• acoustic insulation materials.

Questions

• If you measure a decrease of 3 dB in sound level, how much attenuation is that in terms of percent?
• What types of materials do you think will attenuate low frequencies (20–300 Hz) best?
• What types of materials do you think will attenuate midrange frequencies (300–5,000 Hz) best?
• What types of materials do you think will attenuate high frequencies (above 5,000 Hz) best?

Bibliography

• Here's a great reference on the physics of sound:
  Henderson, T., 2004. "Sound Waves and Music," The Physics Classroom, Glenbrook South High School, Glenview, IL [accessed October 3, 2006] http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/sound/u11l1a.html.
• Here is a good site with information on sound-attenuating materials and construction techniques:
  BRE, date unknown. "Improving Sound Insulation in Homes," Building Research Establishment, Ltd., UK [accessed October 3, 2006] http://www.bre.co.uk/pdf/soundins_homes.pdf.

Materials and Equipment

To do this experiment you will need the following materials and equipment:

• sound system for producing sine wave tones:
  • audio loudspeaker,
  • audio amplifier,
  • CD player;
• audio test CD:
  • the CD must have pure tones (sine waves) over the range of frequencies you wish to test;
  • least expensive one we could find online was $20 if you download and burn it to CD yourself. (Available from: http://www.testaudio.com/testaudio/audio_test_2.asp). Note: Science Buddies has not tested this CD, but it should work for this project.
• sound level meter (e.g., Radio Shack #33-2055, about $50 in October, 2006),
• sound-absorbing materials to test, e.g.:
  • acoustic foam,
  • foam blocks,
  • soundboard,
  • gypsum wallboard,
  • Do a search for "sound insulation" or "acoustic insulation" to locate online sources for evaluating and buying these products.

Disclaimer: Science Buddies occasionally provides information (such as part numbers, supplier names, and supplier weblinks) to assist our users in locating specialty items for individual projects. The information is provided solely as a convenience to our users. We do our best to make sure that part numbers and descriptions are accurate when first listed. However, since part numbers do change as items are obsoleted or improved, please send us an email if you run across any parts that are no longer available. We also do our best to make sure that any listed supplier provides prompt, courteous service. Science Buddies receives no consideration, financial or otherwise, from suppliers for these listings. (The sole exception is any Amazon.com link.) If you have any comments (positive or negative) related to purchases you've made for science fair projects from recommendations on our site, please let us know. Write to us at scibuddy@sciencebuddies.org.

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Experimental Procedure

1. Do your background research to make sure that you are knowledgeable about the terms, concepts and questions above.
2. Select the materials you want to test. The Materials and Equipment section has suggestions, and your background research may turn up additional materials to try.
3. Select at least 6 frequencies to test:
   • 2 low frequencies (20–300 Hz),
   • 2 midrange frequencies (300–5,000 Hz),
   • 2 high frequencies (5,000 Hz and above).
4. Measure the attentuation for each material at each frequency:
   1. Adjust the volume to get a constant sound pressure (e.g., 65 dB SPL) on the sound level meter at a fixed distance (e.g., 0.5 meter) from the speaker.
   2. Place the material to be tested in front of the speaker and measure the sound level again. Record the attenuation.
   3. Repeat for each test frequency.
   4. Repeat for each material to be tested.
5. Are the results what you expected? Why or why not?
6. Can you find common characteristics for materials that do a good job at attenutating sound over a particular frequency range?

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Variations

• Do additional layers of material help?
• How much would it cost? Do an analysis to see which material would have the lowest cost for a given amount of attenuation of a desired frequency range.
• How much space would the insulating materials take up? Do an analysis to see which material would be most efficient per unit volume.
• Advanced. From what you have learned from your background research and the experiment above, how would you design an enclosure to attenuate audio frequencies?

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Related Links

• Science Fair Project Guide
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