Absorption Characteristics of Noise Control Materials

Brad Gassner

10/6/2015

Abstract

A standing wave tube was used to explore the absorption characteristics of various noise control

materials. A sound pressure level (SPL) meter was used to measure the intensity of the sound in the

tube at standing wave maxima and minima for a range of frequencies for a particle board sample. The

normal incidence absorption coefficient 𝛼𝑛 was calculated for each trial and the correlation between 𝛼𝑛

and incident frequency, amount of airspace behind the material, and material thickness are discussed.

The absorption coefficient also depends upon the thickness of the sample. Finally, the effect of airspace

behind a material sample was explored for samples of drywall.

Procedure

The standing wave tube was first qualified by loading no material sample in the test chamber, and the

piston at the end was set to zero displacement. The probe was then used to measure the sound level in

the tube without any excitation signal. Next, a sinusoidal signal of frequencies 125, 250, 500, 1000, and

1600 Hz were input sequentially into the tube. The probe was traversed along the tube and the locations

and values of maximum and minimum pressure levels were recorded. A sample of particle board was

introduced into the standing wave tube and the procedure was repeated. The procedure was again

repeated with an airspace behind the material sample of one and two inches. The particle board sample

was removed and different thicknesses of drywall were inserted into the chamber and the procedure

was repeated for each. Please refer to Mechanical Engineering Systems Laboratory (Lab Manual) for a

step-by-step procedural breakdown.

Results

The tube was qualified by first using no acoustic absorptive material in the test chamber. The data

collected can be seen below in Table 1. The airspace was searched for the first minimum from the

reflective end of the tube. Its location and sound pressure level were recorded. The corresponding

maximum closer to the end of the tube was located and the data points were recorded for this position

as well. It is necessary to note that the last data points obtained below were not collected at 1800 Hz as

stated in the lab manual, but rather at 1600 Hz due to the readout on the sound pressure level

instrument. This frequency was chosen over the next higher 2 kHz frequency due to the fact that at

lower frequencies, the cross-sectional profile of the standing wave in the tube is more closely

approximated by a plane and the irregularities created by the elbow by the speaker are minimized at

lower frequencies.

Table 1: Tube Qualification, No Sample

The absorption coefficients calculated show that there is significant, albeit small, absorption by the

aluminum tube end. This is a baseline measurement that will need to be considered throughout the rest

of this analysis.

A particle board puck was inserted into the sample chamber and the measurements were repeated for

an airspace behind the sample of zero, one, and two inches. See Figure 1 for a chart of the absorption

coefficient calculated for each data point for zero, one, and two inches of air gap behind the sample. The

polynomial trend lines are added simply to help identify the series and trends. It can be seen clearly that

the acoustic absorption characteristics vary widely with the applied frequency and the air gap left

behind the sample of particle board.

Figure 1: Absorption Coefficient vs. Frequency

The absorption coefficient was very high for low frequencies and with air gaps. For the 1600Hz signal,

the absorption coefficient was low for all three air gap setups.

The dependence of the absorption coefficient on thickness of an acoustic material sample was explored

by using several thicknesses of gypsum sheetrock (drywall). We used five samples, but because of the

limited resolution of the measuring equipment available, some of the thicknesses were measured to be

the same thickness. These samples were tested at a frequency of 𝑓 = 1000𝐻𝑧. See Table 2 for the data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 500 1000 1500 2000

Ab

sorp

tio

n C

oef

fici

ent

Applied Frequency (Hz)

Absorption Coefficient vs. Frequency

Zero Inches

One Inch

Two Inches

Poly. (Zero Inches)

Poly. (One Inch)

Poly. (Two Inches)

collected during this portion of the experiment and Figure 2: Absorption Coefficient vs. Sample

Thickness.

Table 2: Absorption Coefficient for Different Thicknesses

Figure 2: Absorption Coefficient vs. Sample Thickness

With an average absorption coefficient of 0.1121 throughout all the samples, it can be seen that drywall

is not a very good absorber of sound energy at 1000Hz. In addition, there were two values measured for

the two thicknesses of .5625in and .625in. This can be due to the errors associated with finding the

maximum and minimum values of the sound pressure. One would expect intuitively a higher absorption

coefficient for a thicker sample, but in general this is not the case here. Drywall is a poor absorber of

sound energy.

Answers to Lab Manual Questions

The first questions in the Lab Manual can be found in section 2.6 Results of Interest, part 3. The

theoretical speed of sound, treating air as an ideal gas, can be calculated to a good approximation as a

function of temperature, given by equation 2.17 (Lab Manual). This speed of sound in the lab on the day

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.5 0.55 0.6 0.65 0.7

Ab

sorp

tio

n C

oef

fici

ent

Drywall Sample Thickness (in)

Absorption Coefficient vs. Sample Thickness

the observations were made to be 1131.8 ft/s. The experimentally determined wavelength was

calculated from the difference between x_min and x_max multiplied by four and the speed of sound

calculated from the wavelength multiplied by the applied frequency. The percent differences between

the ideal gas calculated value and the experimentally determined value can be seen in the chart below,

Table 3: Speed of Sound Calculation and Percent Difference.

Table 3: Speed of Sound Calculation and Percent Difference

For the frequencies of 125, 250, and 500 Hz, the percent differences are very large. The maximum

percent difference is at 250 Hz and is 106%. This shows a very poor estimate of the speed of sound. The

1600 Hz tested frequency shows a very good correlation between the actual and calculated speed of

sound.

Question 4 asks if a frequency of 4000 Hz could be used in this standing wave tube. It could not. We can

expect a cross-sectional plane wave in the tube, theoretically, for frequencies below 2.2 kHz. However,

in practice, 1.8 kHz is the practical limit due to the geometry of the tube. At 4 kHz, the profile of the

sound waves in the tube is no longer planar due, again, to the geometry of the tube and the elbow

where the excitation signal enters the tube. There is simply too much variation to be able to extract any

meaningful result.

Similarly, the geometry of the tube prohibits the use of a 50 Hz signal in the tube. Even at 125 Hz, we

can only fit about one half wavelength in the tube. 50 Hz is out of the question, as less than one quarter

wavelength would fit. This is not enough to be able to locate the minimum and maximum of a period of

the standing wave in the tube, since the wavelength would not fit in the tube!

Sources of Error

The large errors in this experiment and analysis are due to trouble locating the local maxima and minima

of the rectified sine wave due to the peaks and valleys of this wave being flat, i.e. the derivative is

approximately zero. This leads to errors in the positioning of the probe in the tube. In addition, any

sounds in the laboratory, of which there were many, could skew our results, especially if there is any

noise with a regular vibration. The air conditioning in the building was running during the whole

experiment. We measured the sound pressure level in the tube with zero excitation signal. See Table 4:

Measurements of Noise in the Unexcited Tube. We took 12 measurements equally down the length of

the tube.

Table 4: Measurements of Noise in the Unexcited Tube

One final source of error came from the tape measure. Close to the ‘farthest in’ position of the probe,

the resolution of the tape measure was graduated in 32nds of an inch. But further out, it was graduated

in 16ths. Add to that the large indicator on the probe sled and some members of the lab having trouble

reading tape measures, this adds up to be one large potential source of error.

Conclusion

In attempting to quantify the absorptive characteristics of acoustic materials, it is imperative that an

experimental procedure be developed to be able to compare the relative strengths of the incident wave

and the reflected wave. The normal incidence absorption coefficient 𝛼𝑛 is defined as the average

intensity absorbed divided by the average intensity received. By measuring the relative strengths of the

local maxima and minima in the standing wave tube and calculating the standing wave ratio, we can

easily determine the absorption coefficient.

Improvements in data collection could be made by simply explaining better how to use the sound

pressure level meter. There was some difficulty finding the right mode of operation to use and our TA

had to be contacted. One picture in the lab manual would correct this. Additionally, a digital readout of

the position of the probe carriage would be extremely helpful to eliminate guesswork and errors in

reading the tape measure. These can be obtained relatively inexpensively from any machine shop

supplier.

References

Mechanical Engineering Systems Laboratory (Lab Manual). Stutts, Daniel S. et al., Missouri University of

Science and Technology. 2015. Obtained from

http://web.mst.edu/~stutts/ME242/LABMANUAL/ME242Text.pdf . Accessed September 2015.

Dr. Eversman Acoustics Experiment 1.31. Stutts, Daniel S., Missouri University of Science and

Technology. Obtained from canvas by Instructure. Accessed 9/14/2015.

Appendix 1: Sample Calculations

Standing Wave Ratio

𝑆𝑊𝑅 = 10𝐿𝑝𝑚𝑎𝑥−𝐿𝑝𝑚𝑖𝑛

20 = 10122−88.2

20 = 48.98

Normal Incidence Absorption Coefficient

𝛼𝑛 =4 ∗ 𝑆𝑊𝑅

(𝑆𝑊𝑅 + 1)2=

4 ∗ 48.98

(48.98 + 1)2= .07843

Wavelength

𝜆 = 4 ∗ (𝑥𝑚𝑖𝑛 − 𝑥𝑚𝑎𝑥) = 4 ∗ (28.125 − 14.75) = 53.5 𝑖𝑛.

Experimental Speed of Sound

𝑐𝑒𝑥𝑝 =𝜆𝑓

12= 53.5𝑖𝑛.∗ 125 𝐻𝑧 ∗

1

12= 557.3

𝑓𝑡

𝑠

Speed of Sound with Air as Ideal Gas

𝑐 = 20.0457√𝑇𝑐 + 273.15 = 20.0457√23 + 273.15 = 344.97𝑚

𝑠= 1131.8

𝑓𝑡

𝑠

Percent Difference

%𝐷𝑖𝑓𝑓 =|(𝐸1 − 𝐸2)|

. 5 ∗ (𝐸1 + 𝐸2)∗ 100% =

|557.292 − 1131.8|

. 5 ∗ (557.292 + 1131.8)= 68.03%