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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
Costanzo – Nowakowski 2
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.
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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).
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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
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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).
Costanzo – Nowakowski 6
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.
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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.
Costanzo – Nowakowski 8
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
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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
Costanzo – Nowakowski 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
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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.
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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.
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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
Costanzo – Nowakowski 14
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)
Costanzo – Nowakowski 15
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)
Costanzo – Nowakowski 16
-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)
Trial #Sound Level (dB)
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. +)
Costanzo – Nowakowski 17
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
Costanzo – Nowakowski 18
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.
Costanzo – Nowakowski 19
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
Costanzo – Nowakowski 20
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.
Costanzo – Nowakowski 21
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.
Costanzo – Nowakowski 22
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.
Costanzo – Nowakowski 23
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
Costanzo – Nowakowski 24
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.
Costanzo – Nowakowski 25
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