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Costanzo – Nowakowski 1

Introduction

Sound is literally everywhere in the world. Whether it is able to be heard by the

human ear or not, it’s there. The human ear can hear anywhere from 20 Hertz to 20,000

Hertz. Frequencies that are above and below this range cannot be heard by the human ear.

Different materials allow different amounts of sound to travel through them. This is taken

into consideration when building houses or structures near loud areas. When building a

house near an airport or train station, it would be unwise to make it out of glass because

of its low density. The loud noise would travel through the house much easier than it

would if it were made of brick, which has a higher density. Knowing how sound travels

through different materials and at what frequency the sound will travel the fastest can

help people to know how to build those structures. This can also help people in the music

business. Building sound booths and learning how to protect them from loud sounds can

help the company thrive rather than feel threatened.

Several different materials were tested along with different frequencies to see how

they interact and how they affect the level of sound. It is intended to improve upon the

knowledge of sound and what frequencies can travel easier through the materials.

Different pitches were projected through different mediums to see how much sound

travels through. A Design of Experiment (DOE) was then done to see what would affect

the sound level more: medium, pitch, or a combination of the two together.

For the many homes that suffer with loud neighbors or constant construction there

are ways to improve the home so that there is less sound coming in. For example, having

curtains and carpets instead of hard wood floors and blinds can help to reduce sound

inside the house. Also having more shrubbery and trees in the landscape around the house


can help to reduce the amount of sound that hits the house. There are many other things

to sound proof the house. This experiment will help to find what types of materials will

be the best at blocking that sound.


Review of Literature

The experiment that was carried out measured the effect of two factors on the

volume, measured in decibels, of a sound. The first was the frequency of the sound and

the second was the density of the solid material that the sound passed through.

Sounds are defined as vibrations through a medium, such as air and other

materials, that can be heard when they reach a person’s ear. Sound waves are

longitudinal, meaning that the sound particles move along the direction of the wave. This

is important because longitudinal waves expand and compress in series in order for the

waves to move.

Figure 1. Longitudinal Wave (France)

Figure 1 shows a longitudinal wave, which represents a sound wave. When the

wave compresses, the energy increases, causing the molecules to vibrate together in a

wave-like pattern.

One of the most recognizable aspects of sound is its pitch. The pitch of a sound is

determined by the frequency of the sound wave. A pitch is high when the frequency is

high. Individuals with good hearing are able to hear frequencies as low as 20 Hz and as

high as 20,000 Hz. Known as the audible range, as no human can hear above or below

this range (Giancoli 322-24).


Figure 2. Frequencies on a Piano (Caprani)

Every musical note has its own frequency. Figure 2 shows that there is an

exponential relationship between the notes and frequency. The note A4 has a frequency

of 440 Hz and is known as the “standard tuning pitch” (Henderson).

Sound can travel through all states of matter; however, it is transmitted faster

through solids than it is through liquids and gases. This is due to the fact that sound is

essentially just kinetic energy being conducted from molecule to molecule. The kinetic

energy can be transferred faster if the molecules are close to one another, like in solids

and liquids. However, because solids and liquids are denser than gases, less sound will

come through the material. This is because as sound moves through the material, and as it

bounces around all of the molecules, it loses energy. The energy loss causes the sound

level to decrease when it goes through the material and comes out on the other side

(“Material Density and Sound Transmissions”).

Density is a unique physical property for each element and compound. Sometimes

it is referred to as how two different materials differ in “heaviness” when the volume is

constant. When measured, the density will be in mass per unit volume which is most

often shown by grams per cubic centimeter or grams per cubic milliliter. As long as at


least two of the variables, such as mass, density, or volume are known, the other variable

can be calculated (Ophardt).

Density depends on the way the molecules act. Molecules of a solid are more

packed together to keep it solid. They do not have much room to move so they do not

allow other molecules to pass between them. This is why it is hard to easily reform a

solid material. Solids, therefore, have a high density. Liquid substances have molecules

that are spread out enough to effortlessly reshape it. The molecules of a gas are so spread

out that it is easy to move or walk through it. Gases, therefore, have a low density

(Perlman).

Figure 3. Densities of a Solid, Liquid, and Gas (Clark)

Figure 3 shows how the density changes between a solid, liquid, and gas. In the

actual research that was conducted, there were three solids being used; the three types of

matter will better assist in this explanation though. As sound travels through a medium,

the particles must vibrate around and through the medium’s particles. In a solid, it is

easier for sound to travel due to the molecules being tightly packed together. The

molecules in liquids are not as tightly packed together, so the sound cannot travel as

quickly. They have a farther distance to travel so the sound is slower because the

molecules take more time to run into each other. Sound travels the slowest through a gas

because the particles have so much room to move and bump into each other. Because gas

particles are everywhere, sound can be heard from all directions (Edmondson).


Different densities only allow so much sound to pass through the molecules.

Although it is true that when the material’s density is higher the sound will travel through

it with ease, it must also be taken into account that as it travels from particle to particle, it

is losing energy. The amplitude of the sound wave, which is the factor that affects the

volume of the sound, is proportional to the energy within the sound wave. So, as it travels

and loses energy, the amplitude is also decreasing, allowing the sound to be quieter when

it is projected out on the other side. This supports the original hypothesis that states that

the material with the highest density would yield the quietest sound.

As for the interaction between frequency and density, the one thing to remember

is that the frequency of a sound wave stays constant through all mediums. This means

that no matter what material the sound passes through, the frequency will remain the

same. Therefore, the density should not have a significant effect on the frequency, but

should have an effect on the sound level as the problem statement stated that it would

have a significant effect.


Problem Statement

Problem:

How does the frequency of sound waves and density of a solid affect the volume

of sound?

Hypothesis:

If the frequency is at its lowest and the higher density solid is used, the sound will

be quieter than any other trial.

Data Measured:

The independent variables for this experiment are both the frequency measured in

Hertz and the density of material measured in kg/m3. The dependent variable was the

decibel level, or volume, of sound. For the procedure, a sound from a speaker was

projected through a solid. There was then a microphone on the other side of the solid that

will pick up how much sound traveled through the solid. The test that was used was a

two-factor DOE, or design of experiment, which was repeated 10 times. The procedure

had to be done in a quiet room so that no other sounds would interrupt the tone being

played.


Experimental Design

Materials:

iHome 3.5mm Aux Portable Speaker iPhone 5SiPhone n-Track-Tuner App12in x 6in x 3.5in Cardboard Box (1) (Appendix A)18in x 4in x 1/8in Sheet of Balsa Wood7.5in x 5in x 1/16in Sheet of Aluminum Foil20 in x 14 in x 1/8 in Stainless Steel Sheet PanVernier SLM-BTA Sound Level Meter½ in FoamAuxiliary CordTi-Nspire Calculator

Procedure:

1. Using the TI-Nspire randomize function, randomize the trials for the experiment.

There will be 10 DOEs total. Randomize each individual DOE of seven trials.

2. Create the box (as shown in Appendix A) to cover the speaker.

3. Using the auxiliary cord, connect the phone to the speaker to amplify the sound of the

tone. Make sure that the speaker is kept at a constant medium volume. Trials should

also be done in a quiet environment away from outside noise.

4. Place the speaker in the box and line it up with the hole cut out. Tape this down so it

will not move. Leave the tuner on the outside of the box for control of pitch.

5. Align the sheet of balsa wood in front of the hole and speaker. Press the wood against

the hole to make sure no sound escapes.

6. Turn on the decibel reader and allow the pitch to play until the sound level meter

stabilizes. Record the decibel level in the data table.

7. Repeat step 5-6 as needed for each of the different pitches and materials.

Cover BoxSpeakeriPhoneTapeSound Level MeterAluminum FoilBalsa WoodStainless SteelRulerAuxiliary Cord

1

8

9

7

6

5

2


Table 1Variables

Density (kg/m3) Frequency (Hz)

- Standard + - Standard +

Balsa Wood

160

Aluminum Foil

2700

Stainless Steel

3800

220 440 880

Above in Table 1 are the values used in the procedure.

Diagram:

Figure 4.Materials Used in Procedure

Figure 4 above shows the materials used in the procedure. The numbered list on

the right goes along with the numbers in the picture. The procedure to create the box is in

Appendix A.

34

10


Figure 5. Procedure Setup

Figure 5 shows the way the procedure will look. The experimenter starts the tone

playing on the iPhone. That tone is then played through the speaker that is placed under

the box and the sound is sent through the material pressed against the box. The sound

level meter will then pick up the sound and give the final outcome.

Sound Level Meter

Speaker under box


Data and Observations

Table 2Variables

Density (kg/m3) Frequency (Hz)

- Standard + - Standard +

Balsa Wood

160

Aluminum Foil

2700

Stainless Steel

3800

220 440 880

The independent variables that were to be used throughout the process are shown

above in Table 2. The three different materials used to represent different densities was

balsa wood, aluminum foil, and stainless steel. The three different tones used for

frequency were 220, 440, and 880 Hz.

Table 3Data Collected

RunsDOE

1DOE

2DOE

3DOE

4DOE

5DOE

6DOE

7DOE

8DOE

9DOE

10

AverageSound Level

Decibels

Density

Kg/m2

FrequencyHertz

+ + 80.4 81.2 85.3 78.9 83.0 81.2 77.7 78.0 83.6 80.5 81.0

+ - 63.4 64.1 64.6 64.3 64.0 65.7 64.4 62.8 64.1 64.2 64.2

- + 87.1 83.6 84.6 82.7 82.6 83.3 82.7 84.0 83.0 86.2 84.0

- - 62.1 63.3 62.1 61.7 61.4 62.1 58.1 63.2 67.0 61.3 62.2

Table 3 above shows the data collected for the 10 DOE’s that were performed.

The averages are shown and were the numbers used to calculate the later tests. Most of

the runs had consistent data with some that were just a little off but should not affect the

data.


Table 4Observations

Date Observations

1-May

Made markings on box so would hold same spot each time for repetition

Some background noise but should not affect data

Box still moved a little when material placed against it. Extra tape added

Speaker was open for all trials

Researcher One held the material against the box every time

Researcher Two played the tone each time

All trials finished in one day

Pictures and video will be taken tomorrow

The standard noise without the material was equal to 88.5

6-May

All trials that did not use the high material were redone

Standard and low material were flipped because densities were wrong

Some small background noise but should not affect data

Speaker open and box taped down

Researcher One held against box

Researcher Two played noise

Table 4 has the observations taken during trials. All trials were completed on the

first day. The researchers then realized that the low material and the standard material

were wrong and need to be flipped. The trials that needed to be fixed were redone and the

same precautions were done on both days such as taping everything done and being in the

same room.


Data Analysis and Interpretation

The data collected was analyzed using a two-factor Design of Experiment. Each

DOE had three trials of standards. The standards were used throughout the experiment

not only to compare data from other values, but also to reduce confounding from any

lurking variables. The trials were randomized to ensure that all of the treatment groups

were similar. Moreover, the DOE’s were replicated to ensure that the data was consistent

throughout the experiment.

The two factors that were tested are the frequency of a sound and the density of

the solid. The response variable is the sound level, in decibels, of the sound travelling

through a given solid. The two factors were tested to see if there was a significant effect

on the sound level of the sound.

Table 5Design of Experiment Values

Frequency (Hz) Density (kg/m³)- Standard + - Standard +

220 440 880Balsa Wood

Aluminum Foil

Stainless Steel

130 2700 8000

Table 5 shows the experimental values for the density and frequency. The

standard value for density was 2700 kg/m3, which is the density of aluminum foil. The

standard value for frequency was 440 Hz, the note A4, which is standard tuning pitch.

Table 6Effect of Frequency

Frequency (Hz)

- +

62.23 83.98

64.16 80.98


63.195

82.48

Table 6 shows the effect of the first factor, frequency. The average values of

sound level for both the low and high values of frequency are shown bolded at the bottom

of the table. On average, when a low frequency was played through the speaker, the

sound level was 63.195 decibels, and when a high frequency was played, the sound level

was 82.48 decibels.

Figure 6. Effect of Frequency

Figure 6 shows the graph of the effect of frequency. The difference in sound level

was 19.285 decibels. This represents the effect of frequency on sound level.

Table 7Effect of Density

Density (kg/m³)- +

62.23 64.16

83.98 80.98

73.105

72.57

Table 7 shows the effect of the second factor, density. The average values of

sound level for both the low and high values of density are shown bolded at the bottom of

-1 10

20

40

60

80

Frequency (Hz)

Soun

d L

evel

(dB

)

(1, 82.48)

(-1, 63.195)


the table. On average, when a sound was played through a material with a low density,

the sound level was 73.105 decibels, and when a sound was played through a material

with a high density, the sound level was 72.57 decibels.

Figure 7. Effect of Density

Figure 7 shows the graph of the effect of frequency. The difference in sound level

was -0.535 decibels. This represents the effect of density on sound level.

Table 8Table of Averages

Density (kg/m³)

(-) 160

(+) 3800

Frequency (Hz)

Sound Level (dB)

(+) 880

83.98

80.98

Sound Level (dB)

(-) 220

62.23

64.16

Table 8 shows the table of averages. These are the average values for sound level

from each run. This table was then used to calculate the interaction effect of frequency

and density on the sound level.

-1 10

20

40

60

80

Density (kg/m³)

Soun

d L

evel

(dB

) (1, 72.57)(-1, 73.105)


-1 10

20

40

60

80

Density (kg/m³)

Soun

d L

evel

(dB

)(Freq. -)

(1, 80.98)

(-1, 83.98)

(1, 64.16)(-1, 62.23)

Figure 8. Interaction Effect

Figure 8 shows the graph of the interaction effect of frequency and density on the

sound level. The two line segments are not parallel, indicating a possible interaction. The

difference of sound level between the two average values when the high frequency was

played is -3. This was then divided by 2 to get the slope, which is -1.5. The difference of

sound level between the two average values when the low frequency was played is 1.93.

This was then divided by 2 to get the slope, which is 0.965. The difference of the slopes

is -2.465, which represents the interaction effect.

Table 9Standard Runs

Trial #Sound Level (dB)



1 70.3 23 71.7 48 71.15 73.6 28 69.6 51 70.87 73.0 30 72.1 55 70.28 71.8 31 71.8 56 71.3

10 75.7 32 71.2 59 69.813 77.1 37 70.6 60 71.516 72.2 38 69.5 61 70.617 75.8 41 71.2 65 70.019 74.3 43 71.9 66 68.222 70.2 46 71.4 69 72.7

Table 9 shows the standard trials that were carried out during the experiment. The

range of standards was 8.9.

(Freq. +)


0 5 10 15 20 25 30505560657075808590

Trial

Soun

d Le

vel (

dB)

Figure 9. Standard Runs

Figure 9 shows the graph of standard runs. The graph seems to be fairly linear

with no distinct pattern over time. The little variability helps to confirm that the results of

the data are reliable.

-20 -15 -10 -5 0 5 10 15 20 250

0.050.1

Dot Plot of Effects

Figure 10. Dot Plot of Effects

Figure 10 shows the dot plot of effects, where FD is the interaction effect of

frequency and density, D is the effect of density, and F is the effect of frequency. The two

lines represent twice the range of standards on both sides of zero. These are used to

determine which effects are significant. An effect is significant if it is greater than twice

the range of standards on the positive end or less than twice the range of standards on the

negative end. Since the range of standards is 8.9, twice the range of standards is 17.8.

FD D F

17.8-17.8


FREQUENCY :2 (8.9 )=17.8<19.285

DENSITY :17.8>−0.535

INTERACTION :17.8>−2.465

Figure 11. Test of Significance

Figure 11 shows the test for significance. The effect of frequency is significant

because its value, 19.285, is greater than twice the range of standards. On the other hand,

the effect of density and the interaction effect are not significant because they fall

between the boundary of twice the range of standards on both the positive and negative

ends.

Refer to Appendix B to see the prediction equation and the parsimonious

prediction equation.


Conclusion

To conclude, the original hypothesis that the lowest frequency and the highest

density solid will produce the quietest sound was rejected. It was found throughout the

experimental process, on average, that the lowest frequency and the lowest density

produced the quietest sound, with an average of 62.23 dB, which is 1.93 dB lower than

that of the values from the original hypothesis. Ten two-factor design of experiments

were used and averaged to calculate the factor that would be significant in producing the

different levels of sound. Frequency was found to be the only factor that was significant

in doing this. However, this opposes the original hypothesis that both density and

frequency would be significant factors.

The results of the DOE showed that the lowest frequency paired with the lowest

density yielded the lowest decibel level. This also opposes the original hypothesis that the

highest density would produce the lowest decibel level. This is due to the structure of the

balsa wood, which was the material with the lowest density. The wood was not of good

quality as it was very thin and soft. It was not completely solid and it had a lot of air

pockets. So when a sound was played through it, although the sound waves were freer

given the empty space, they lost energy. This is due to the fact that the sound waves were

reflected off of all of these air pockets over and over. These reflections that occurred

reduced the sound waves’ energy. The loss of energy yielded a lower decibel level when

the sound waves were actually able to get through the material. This supports why the

original hypothesis was wrong.

One of the largest outside factors was the background noise. The sounds of cars

constantly driving by and the continual buzzing noises were picked up by the sound level


meter, so the room was never completely silent. These outside sounds mixed with the

sounds that were coming out of the speaker, making the sound level meter unable to

record an accurate measure. This does not agree with accepted theories that say that

sounds played through higher density materials would have a lower decibel level. Some

of the trials, therefore, may still be unreliable, which may be the reason why the original

hypothesis that both frequency and density would be significant factors was rejected.

Other lurking variables may have been factors in the weaknesses of the

experimental process. There could have also been the error that the materials were not

perfect in their role. What is meant by this is that the box could have been better

constructed or there could have been better suited materials and how they were held

If further research were to be conducted, better materials would be used. The

quality of the balsa wood used was very poor, as mentioned earlier, so getting thicker

balsa wood may help in getting more valid results in the DOE. Also, the aluminum

sample used was aluminum foil that was folded to make it thicker. An actual, thick

sample of smooth aluminum could have been used for better results as the folds and

creases in the aluminum foil made the thickness of the sample inconsistent, which could

have again affected how the sound travelled through it and how it was received by the

sound level meter. Finally, a sound proof room would prevent any unwanted sound from

being received by the sound level meter, as the outside noise affected the original

experiment and gave invalid results in the DOE.

All in all, this research would help the community living near airports, train

stations, big concert stages, or any area that would produce large amount of noise.


Knowing how to protect the home and how to sound proof it would help life to be more

pleasant. With this knowledge of how frequency and density of materials interact, people

will see what kind of material they should use depending on what type of noise they live

by. This will also help businessmen in the music industry. They can now produce better

music with the knowledge of how to create their sound booths.


Acknowledgements

We would like to give thanks to Mrs. Rose Cybulski for formatting and writing

help, Mrs. Christine Tallman for checking the math calculated, Mr. Greg McMillan for

teaching and helping throughout the experimental process, and our parents for their

support. Thanks also to Mr. Scot Acre for the help with the DOE.


Appendix A: Creating the Box

To create the box used in Figure 4 for the materials and the procedure is shown in

Figure 12 below.

Figure 12. Cover Box

Materials:

12in x 6in x 3.5in Cardboard BoxMasking TapeScissors½ in Foam of any kind

Procedure:

1. Use the scissors to cut a circular hole in one side of the box. This will be where the sound is coming out of.

2. Then cut a small notch in the bottom of the side of the box. This will allow the wire to go inside the box to the speaker and will still make sure the box is flat on a table.

3. Cut the foam so that there is a piece that fits each of the inside walls of the box.

4. Use the tape to tape the foam inside the box so that it fits tightly together. Make sure the foam does not cover the hole cut out in step 1.

Speaker will be placed inside box.

Foam


Appendix B: Prediction Equations

Y=72.8375+ 19.2852

(Freq . )+−0.5352

( Dens . )+−2.4652

(Freq .)(Dens.)

Figure 10. Prediction Equation

Figure 10 shows the prediction equation for the data. The grand average for all

trials was 72.8375, and all of the effects are included.

Y=72.8375+ 19.2852

(Freq.)

Figure 13. Parsimonious Prediction Equation

Figure 13 shows the parsimonious prediction equation. It shows only the grand

average along with any of the effects that were found to be significant. Only the

frequency of the sound was significant, so no other effects were included.


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<http://www.physicsclassroom.com/class/sound>.

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