Title: Effect of Thickness of the Material on the Transmitted Sound Level
Research Question: To what extent does the material thickness (0.10mm, 0.25mm, 0.30mm,
0.50mm, 0.70mm) have an impact on the sound level (dB) that is transmitted through the
material (Aluminum sheets) by calculating the absorption coefficient in a home-made
impedance tube?
Subject: Physics
Word Count: 3880
i
Table of Contents
Glossary ............................................................................................................................... iii
Abbreviations ........................................................................................................................ v
1.
Introduction ................................................................................................................... 1
1.1 Background Theory ..................................................................................................... 2
1.2 Experimental Hypothesis ............................................................................................. 5
2.
Methodology .................................................................................................................. 6
2.1 Apparatus Required ..................................................................................................... 6
2.2
Experimental Setup ................................................................................................. 7
2.3 Variables ..................................................................................................................... 7
2.4 Experimental Procedure: Construction of Impedance Tube ........................................ 10
2.5 Experimental Procedure: Material Thickness (mm) vs Sound Level (dB) ................... 11
3.
Data Analysis ............................................................................................................... 12
3.1 Graphical Representation of the data in SPARKvue Software .................................... 12
3.2 Raw Data ................................................................................................................... 13
3.3 Processed Data........................................................................................................... 15
4.
Conclusion ................................................................................................................... 18
5.
Evaluation .................................................................................................................... 19
5.1 Limitations ................................................................................................................ 19
5.2 Improvements ............................................................................................................ 20
5.3 Extensions ................................................................................................................. 21
6.
Bibliography ................................................................................................................ 22
7.
Appendices .................................................................................................................. 24
ii
Glossary
1.
Reflection1:
It is the abrupt change in the direction of propagation of a wave that strikes the
boundary between different mediums.
2.
Refraction2:
It is the bending of a wave when it passes from one medium to another. The bending
is caused due to the differences in density between two substances.
3.
Diffraction3:
It is the spreading of waves with respect to an aperture or obstacle.
4.
Interference4:
It is the phenomenon that occurs when two waves meet while travelling along the
same medium. Interference causes the medium to take on a shape that results from the
net effect of the two individual waves upon the particles of the medium.
5.
Transmission5:
It is the passage of electromagnetic radiation through a medium.
1
Augustyn, Adam. "Reflection | Definition, Types, Examples, & Facts." Encyclopedia Britannica, Britannica,
www.britannica.com/science/reflection-physics. Accessed 5 Dec. 2021.
2
"Refraction - Definition, Causes, Laws, Refractive Index, Examples, Applications, Video, Solved Problems, and
FAQs." BYJUS, 18 Feb. 2021, byjus.com/physics/refraction-of-light/. Accessed 4 Dec. 2021.
3
---. "Diffraction." Encyclopedia Britannica, www.britannica.com/science/diffraction. Accessed 8 Dec. 2021.
4
"Physics Tutorial: Interference of Waves." The Physics Classroom,
www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves. Accessed 30 Nov. 2021.
5
"What is the Transmission of a Wave?" BYJUS, 5 Jan. 2021, byjus.com/jee-questions/what-is-thetransmission-of-a-wave. Accessed 16 Nov. 2021.
iii
6.
Intensity6:
It is defined as the rate at which a wave transfers its energy divided by the area over
which the energy is being spread.
7.
Decibel7:
It is the logarithmic unit used to measure sound level.
8.
Absorption Coefficient8:
It is the value which describes the amount of a wave that is absorbed by a material of
a given thickness. It is represented by the Greek letter 𝛼.
9.
Zero Error9:
They are errors caused by faulty equipment that does not reset to zero properly.
10.
Sound Level10:
It refers to the various logarithmic measurements of audible vibrations.
6
"Wave Intensity." ScienceDirect.com | Science, Health and Medical Journals, Full Text Articles and Books,
www.sciencedirect.com/topics/mathematics/wave-intensity. Accessed 28 Nov. 2021.
7
"DB: What is a Decibel?" Physics Animations and Film Clips: Physclips, School of Physics, Sydney, Australia,
www.animations.physics.unsw.edu.au/jw/dB.htm. Accessed 25 Nov. 2021.
8
"The Absorption Coefficient: Definition & Calculation." Study.com, 11 March 2021,
study.com/academy/lesson/the-absorption-coefficient-definition-calculation.html. Accessed 29 Nov. 2021.
9
"Random Errors - Obtaining, Analysing and Evaluating Results – WJEC - GCSE Physics (Single Science) Revision
- WJEC - BBC Bitesize." BBC Bitesize, www.bbc.co.uk/bitesize/guides/z8fq6yc/revision/5. Accessed
17 Dec. 2021.
10
"Sound Intensity and Sound Level | Physics." Lumen Learning – Simple Book Production,
courses.lumenlearning.com/physics/chapter/17-3-sound-intensity-and-sound-level. Accessed 30 Nov. 2021.
iv
Abbreviations
𝑑𝐵 → 𝑑𝑒𝑐𝑖𝑏𝑒𝑙
𝐼 → 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝐼𝑜 → 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝑑𝐵𝐴 → 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑙𝑒𝑣𝑒𝑙
𝛼 → 𝑠𝑜𝑢𝑛𝑑 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝐼𝑎 → 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝐼𝑖 → 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
v
1. Introduction
Waves are ‘constantly changing disturbances that carry energy through a medium.’ Waves
show four types of phenomena which are Reflection, Refraction, Diffraction, and
Interference. When learning about the sound waves in IB Physics, the concepts and properties
of Wave Phenomena were introduced but we never learned about the transmission of waves. I
always perceived that a wave does not travel completely through a material and that some of
this wave is left behind. I realized that the amount of wave passing through a material,
changes with respect to several conceptions such as the material itself, thickness of the
material and so on. This made me do more research on why this phenomenon was occurring.
After going through few research papers11, I found that the incident of sound waves passing
through different solids is termed as “Transmission of Waves” in physics.
I always considered the theory of diffraction of sound waves in which they spread out by
virtue of passing through a narrow aperture or opening and thus providing the sound to a
larger radius depending on the wavelength of the incident sound wave and the width of the
slit or the distance between the slits. But transmission of sound was more about the travelling
of sound waves not around a solid structure but instead through it. With my increasing
passion towards this concept of sound waves, I wanted to explore more about this approach.
So, I started researching about how the transmission of sound waves materialize, what is the
amount incident sound waves transmitted through, what are the causes for lower or higher
amounts of sound waves transmitted, and so on. During my research, I recognized that at
most aspects of transmission of sound waves, the type of material along with its thickness
played a significant role in this concept. So, I kept exploring for materials that easily transmit
11
Ju, Liehong, et al. "EXPERIMENTAL RESEARCH ON COEFFICIENT OF WAVE TRANSMISSION THROUGH
IMMERSED VERTICAL BARRIER OF OPEN-TYPE
BREAKWATER." https://journals.tdl.org/icce/index.php/icce/article/download/1444/pdf_133/,
journals.tdl.org/icce/index.php/icce/article/download/1444/pdf_133/.
1
sound waves through them. With consistent research, I could conclude that Aluminum sheets
have a high transmission rate12 when sound waves are passed through them.
Along with thickness of materials, the distance between the sound source and the position of
the material also has an impact on the transmission of sound waves through it. This
phenomenon also explains why loud sounds from the houses above sound to be louder when
compared to the same amount of sound coming from downstairs.
Considering the thorough research and understanding on the concept of ‘transmission of
sound and the effect that materials with different thicknesses have on the absorbance and
reflectance of sound waves,” now I wanted to find out more about the factors ‘that affect the
change in the sound level, as the incident sound wave passes through a solid medium.” For
my Extended Essay, I opted to authenticate this topic by conducting an experiment to find out
the change in the Sound Level that is transmitted through varied materials of different
thicknesses. With the help of this experiment, I will be able to prove the “relationship
between thickness of the material and sound level that is transmitted through the
material.” While exploring through this experiment, I will also be able to correlate the Sound
Level to the sound absorption coefficient.
1.1 Background Theory
A sound wave can be classified as an energy that is propagating through a medium away
from the source of the sound. When a sound wave changes its medium or passes through a
different matter or equipment, vibrations that are produced due to the flowing sound particles
disrupt the surroundings and affect the particles adjacent to them and so forth. A sound wave
usually disperses in all directions and as the distance between the wave and the sound source
12
Huang, Yike, et al. "Sound Transmission through Aluminum Framings of Window, Door and Facade
Systems." DEGA Publikationen, ICA 2019, 13 Sept. 2019, pub.degaakustik.de/ICA2019/data/articles/001273.pdf. Accessed 30 Nov. 2021.
2
increases, the intensity of the sound wave gradually reduces, reducing the loudness of the
source.
Although the unit for loudness or intensity of sound waves is watts per meter squared, it is
measured in decibels (dB). A decibel is defined as ‘a unit for expressing the ratio between
two physical quantities, usually for measuring the relative loudness of sounds.’13 One decibel
is calculated as:
𝐼
1 𝑑𝐵 = 10𝑙𝑜𝑔10 [𝐼 ] 14
𝑜
(1)
𝐼 → 𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑆𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝐼𝑜 → 𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑆𝑜𝑢𝑛𝑑 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 → 1 × 10−12 𝑊𝑚−2
Sound waves travel at different speeds in different media. For example, speed of sound is
much faster in solids when compared to liquids or gas. Transmission of sound in solids is
faster due to the phenomenon that the arrangement of molecules in solids is tightly packed
which allows the vibrations caused by sound to easily transmit, whereas the molecules are
located farthest from each other in gases resulting in slower transmission of sound.
This essay with focus on one of these phenomena of sound waves which is transmission.
Transmission of sound waves refers to the propagation of the disturbances caused through a
medium.15 In order to find the relationship between the transmitted sound and thickness of
the material, the coefficient of sound absorption can be used. Sound absorption refers to
depletion of sound when it is passed through a material. A minor part of the sound is
absorbed by the material and some of the energy is lost due to partial reflection, the
13
Gregersen, Erik. "Decibel | Definition, Formula, & Facts." Encyclopedia Britannica,
www.britannica.com/science/decibel
14
Biezen, Michel V. "Physics - Mechanics: Sound and Sound Waves (9 of 47) Decibel Scale
Conversion." YouTube, 7 Oct. 2013, youtu.be/h5HIsz1RmH8.
15
"Sound Transmission." Encyclopedia.com | Free Online Encyclopedia,
www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/sound-transmission.
3
remaining is transmitted through it. The coefficient of absorption can be used to define the
ratio of the sound intensity absorbed to the incident sound intensity.
𝐼
𝛼 = 𝐼𝑎 16 …………………………….. (2)
𝑖
In this equation:
𝛼 = 𝑠𝑜𝑢𝑛𝑑 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝐼𝑎 = 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝐼𝑖 = 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
In theory, increasing the thickness of a material should decrease the magnitude of sound
transmitted. Subsequently, the magnitude of absorbed sound increases, which results in a
larger value of the sound absorption coefficient because the sound waves must travel a longer
path through the material, losing more kinetic energy.
In order to find the intensity of the absorbed sound, to find the sound absorbed coefficient,
experimentally, equation (1) was modified to obtain equation (3):
𝐼
𝑑𝐵𝐴 = 10 × 𝑙𝑜𝑔 [ ]
𝐼𝑜
𝑑𝐵𝐴
𝐼
= 𝑙𝑜𝑔 [ ]
10
𝐼𝑜
𝑑𝐵𝐴
𝐼
10 10 = [ ]
𝐼𝑜
𝑑𝐵𝐴
𝐼 = 𝐼𝑜 × 10 10 …………………………….(3)
16
Engineering ToolBox, (2003). Sound - Room Absorption Coefficients. [online] Available at:
https://www.engineeringtoolbox.com/accoustic-sound-absorption-d_68.html
4
Equation (3) can be substituted in equation (2) to formulate the following: Considering 𝐼 = 𝐼𝐴 , where 𝐼𝐴 = 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
𝛼=
𝐼𝐴
𝐼𝑜
𝑑𝐵𝐴
𝛼=
𝐼𝑜 × 10 10
𝑑𝐵𝑖
𝐼𝑜 × 10 10
𝜶 = 𝟏𝟎
𝒅𝑩𝑨−𝒅𝑩𝒊
𝟏𝟎
……………………...(4)
𝛼 → 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙
𝑑𝐵𝐴 → 𝑠𝑜𝑢𝑛𝑑 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑙𝑒𝑣𝑒𝑙
𝑑𝐵𝑖 → 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑠𝑜𝑢𝑛𝑑 𝑙𝑒𝑣𝑒𝑙
1.2 Experimental Hypothesis
-
With an increase in thickness of a material (aluminum sheets), there is a proportional
decrease in the transmitted sound level, hence, increasing the sound absorption
coefficient of the material. This phenomenon will occur because the sound waves are
forced to travel through a longer path as the thickness of the material increases,
resulting in an increased loss of energy and higher absorbing capacity of the material.
5
2. Methodology
2.1 Apparatus Required
S. no.
Apparatus
Quantity
Least Count
Uncertainty
Measuring Apparatus
1
Stopwatch
1
0.01 s
± 0.01s
2
Wooden Ruler
1
0.1 cm
± 0.05 cm
3
Screw Gauge
1
0.001mm
± 0.0005 mm
4
Sound Level Sensor
1
40.0dB
± 0.1dB
5
Laptop with SPARKvue
1
-
-
Software installed
Experimental Apparatus
6
PVC Pipes
1
± 0.05cm
7
Aluminum Sheets
5
± 0.005 mm
8
Masking tape
3
-
-
9
Hacksaw
1
-
-
10
Polystyrene sheets
(thermocol)
2
-
-
Table 1: Apparatus Required for the experiment
6
2.2 Experimental Setup
Figure 1: Setup of the Experiment with labelled apparatus
2.3 Variables
Independent Variable
-
Thickness of the Material:
o For this investigation, 5 thickness of the same material (aluminum sheets) will
be taken which are 0.10mm, 0.25mm, 0.30mm, 0.50mm and 0.70mm.
o A screw gauge with least count of 0.01mm will be taken to measure the
thickness of the material and the zero error from the gauge will be eliminated
before calculating the thicknesses of aluminum sheets.
Dependent variable
-
Sound Level (dB):
o To measure the sound level that is transmitted through the material in the tube,
a sensor is attached at the other end of the tube which detects the change in the
sound level and records the values of sound level in a tabular and graphical
manner.
7
Control variable
Controlled Variable
Why and how is the variable controlled?
Dimensions of the Tube17
- The dimensions of the tubes used for the entire experiment
were 100cm in length and had a 2cm radius.
- To reduce the uncertainty produced, 3 pipes were cut into
100cm pieces and were then cut accordingly at 30cm, 40cm
and 50cm to place the materials in between.
- Since the change in the radius and length of the tube has
an impact on the amount of sound that passes through the
material, the tube had to be of the same dimensions for the
experiment to work and for the evaluation of data to be
accurate.
Frequency of the Source18
- The frequency of the source was fixed to 2000Hz and was
passed through the material.
- To stabilize the frequency at which the sound was sent
through the tube and the material, an online tone generator
was used which endlessly produces the sound of the
specified frequency.
- Using this tool helped reduce the uncertainties and aided
in sustaining accurate results for the investigation.
Source of the sound
- To curtail the uncertainties formed, the source of the
sound for the entire experiment was from a single Bluetooth
earphone which was small enough to fit through the tube
and produce sound continuously.
- Also, this earphone was charged regularly between each
independent variable to provide a smooth specified
frequency.
17
Stinson, Michael R. "The Propagation of Plane Sound Waves in Narrow and Wide Circular Tubes, and
Generalization to Uniform Tubes of Arbitrary Cross‐sectional Shape." Scitation: Acoustical Society of America,
4 June 1998, asa.scitation.org/doi/10.1121/1.400379. Accessed 23 Oct. 2021.
18
"14.1 Speed of Sound, Frequency, and Wavelength." Texas Gateway, www.texasgateway.org/resource/141speed-sound-frequency-and-wavelength. Accessed 17 Nov. 2021.
8
Material19
- Aluminum sheets of different thickness were used for this
experiment as aluminum is a great factor for transmission of
sound waves.
- Small pieces of radius 2cm were cut from sheets of
aluminum to use in this experiment.
Software and Sensor Used
- For the entire experiment, the Pasco PASPort Sound Level
(PS-2140) sensor along with the PASCO SPARKvue were
used.
- This sensor detected the change in the background sound
level to the sound level which was produced with the
introduction to the sound source.
- This sensor also graphed the increase in the sound level in
the software and provided the data in a tabular form to
analyze.
Background Sound Level
- Assuming the range of the sensor used was from 40dB to
90dB, I have conducted my experiment in a quiet room with
acoustic panels to the walls to reduce the background sound
level.
- For the entire experiment, the background sound level was
kept standard around 40dB to acknowledge the change in
the sound level when the source was introduced.
Number of trials taken
- To reduce the uncertainty produced, each experiment with
each independent variable was conducted 5 times and the
data is collected in a tabular and graphical format to analyze
and approximate the mean value and final change in sound
level.
Material of the tube20
- Since absorption capacity changes from material to
material, for this experiment, I have taken polyvinyl
19
Sun, J. Q., and Priya Thamburaj. "(PDF) Effect of Material and Geometry on the Sound and Vibration
Transmission Across a Sandwich Beam." ResearchGate, 1 Apr. 2001,
www.researchgate.net/publication/239660643_Effect_of_Material_and_Geometry_on_the_Sound_and_Vibra
tion_Transmission_across_a_Sandwich_Beam. Accessed 29 Nov. 2021.
20
Zhu, Xiaodong, et al. "Fig. 1. The Impedance Tube System for Sound Transmission
Measurements...." ResearchGate, 1 Jan. 2021, www.researchgate.net/figure/The-impedance-tube-system-forsound-transmission-measurements-a-Typical-Transmission_fig1_270503154. Accessed 19 Nov. 2021.
9
chloride pipes (PVC).
- The reason to choose these pipes to make the tube was
that PVC will reduce the sound reflection and reverberation
reducing the sound waves from escaping through the pipe
and thus reducing the sound level.
Distance of the material
- The entire experiment was conducted 3 times with
from the sound source21
different material thicknesses at 3 different distances
(30cm, 40cm, 50cm) of the material from the sound source.
- The distance of the material from the sound source was
kept as a control variable to analyze the change in the
transmitted sound level and the effect of distance on the
same. This experiment was conducted by taking 3 pipes
with 3 individual distances from the sound source.
Table 2: Controlled Variables
2.4 Experimental Procedure: Construction of Impedance Tube
-
Since the original design of an Impedance tube22 was constructed in such a way to
detect the reflected rays reflected from the material, the impedance tube designed for
this experiment had to be tweaked a little to satisfy the transmission of sound waves
and be caught on the other end of the material using a sound level sensor.
1. Initially, 3 PVC pipes were taken and cut into pieces of each of length 100 cm.
2. These pipes were then cut and smoothened in the corners to place the sound level
sensor and the sound source.
21
Aylor, D. "Sound_Propagation." SFU.ca - Simon Fraser University, www.sfu.ca/sonic-studiowebdav/handbook/Sound_Propagation.html. Accessed 19 Nov. 2021.
22
Suhanek, Mia. "(PDF) Student Project of Building an Impedance Tube." ResearchGate, 1 June 2008,
www.researchgate.net/publication/5325257_Student_project_of_building_an_impedance_tube.
10
3. Then, small craters were made at both the ends of all the three pipes in the shape of
sensor.
4. After the craters were made, the sensor was fixed to the end by gluing the sensor to a
piece of polystyrene sheet (thermocol sheet) and hooked into the pipe.
5. Then, the Bluetooth earphone was placed into the pipe and that end of the tube was
covered using more polystyrene sheet (thermocol sheet).
6. Now, 5 different thickness of aluminum sheets were taken.
7. Using a screw gauge, these sheets were marked with different thicknesses (0.10mm,
0.25mm, 0.30mm, 0.50mm and 0.70mm) and were then cut into circular shapes with
radius of 2cm.
2.5 Experimental Procedure: Material Thickness (mm) vs Sound Level (dB)
1. Now, a pipe of length 30cm was taken for the experiment to be conducted.
2. Aluminum sheets of the thickness 0.1mm was taken and connected to the 30cm pipe.
3. Then, the other part of the pipe with 70cm length was attached to this pipe using
masking tape.
4. Using the online tone generator, the sound with 2000Hz frequency was sent through
the material of thickness 0.1mm.
5. SPARKvue software was used to detect the change in the sound level before passing
the sound, during sound transmission and after the sound was passed.
6. Steps 1-5 were then repeated for material thicknesses 0.25mm, 0.3mm, 0.5mm and
0.7mm.
7. With the help of SPARKvue, the data obtained was then converted to a graphical
form for better analysis of the effect of material thickness on the sound transmission
through it.
11
8. Finally, the graph from the experiment was observe the change the difference in
sound level (dB) generated with the change in the material thickness of aluminum
sheets.
3. Data Analysis
3.1 Graphical Representation of the data in SPARKvue Software
Figure 2: Graph showing transmitted sound level(dB) for all the 5 thicknesses
The data from sensor was recorded in SPARKvue software in a tabular format. All the trials
from this table were then reformed into a singular table to process and achieve sound
absorption coefficient to relate the thickness of material to the sound level transmitted.
12
3.2 Raw Data
Sound Level (±0.1 dB)
Material
Thickness
(±0.005
mm)
Distance of
the material
from the
source
(±0.1cm)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Mean Sound
Level
0.1
30
57
58
57
57
57
57.2
40
59
60
59
59
60
59.4
50
63
63
62
62
62
62.4
30
52
53
52
52
52
52.2
40
56
57
56
56
56
56.2
50
59
58
59
59
59
58.8
30
48
48
49
48
47
48.0
40
50
51
51
51
51
50.8
50
57
57
57
57
57
57.0
30
46
45
45
45
45
45.2
40
48
49
48
48
48
48.2
50
53
54
54
54
54
53.8
30
44
43
43
43
43
43.2
40
45
45
46
45
45
45.2
50
48
48
48
48
49
48.2
0.25
0.3
0.5
0.7
Trials
Table 3: Raw Data with Material Thickness and Sound Level
13
Sample Calculations:
1. Mean Sound Level:
𝑀𝑒𝑎𝑛 =
𝑆𝑢𝑚 𝑜𝑓 𝐴𝑙𝑙 𝑡ℎ𝑒 𝑡𝑟𝑖𝑎𝑙𝑠 57 + 58 + 57 + 57 + 57 286
=
=
= 57.2
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
5
5
2. Absorbed Sound Level:
𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 = 90 − 𝑚𝑒𝑎𝑛 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑙𝑒𝑣𝑒𝑙
𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑑 𝑠𝑜𝑢𝑛𝑑 𝑙𝑒𝑣𝑒𝑙 = 90 − 57.2 = 32.8
3. Uncertainty in Mean Sound Level:
∆𝐿 =
𝑆𝑜𝑢𝑛𝑑 𝐿𝑒𝑣𝑒𝑙𝑚𝑎𝑥 − 𝑆𝑜𝑢𝑛𝑑 𝐿𝑒𝑣𝑒𝑙𝑚𝑖𝑛
2
∆𝐿 =
58 − 57 1
= = ±0.5
2
2
4. % Uncertainty in Mean Sound Level:
%𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 =
%=
∆𝐿
× 100
𝐿
0.5
× 100 = ±0.87%
57.2
5. Absorption Coefficient:
𝜶 = 𝟏𝟎
𝒅𝑩𝑨 −𝒅𝑩𝒊
𝟏𝟎
𝛼 = 10
32.8−90
10
−57.2
𝛼 = 10 10 = 10−5.72
𝛼 = 1.905 × 10−6
14
3.3 Processed Data
Material
Distance
Mean
Absorbed Uncertainty
Thickness
of the
Observed
Sound
(±0.05mm)
material
Sound
Level
from the
Level
(±0.1L)
source
(±0.1L)
%
Absorption
in Sound
Uncertainty
Coefficient
Level
in Sound
(𝟏𝟎−𝟔 )
Level
(±0.1cm)
0.1
0.25
0.3
0.5
0.7
30
57.2
32.8
0.5
0.87
1.91
40
59.4
30.6
0.5
0.84
1.15
50
62.4
27.6
0.5
0.80
0.57
30
52.2
37.8
0.5
0.96
6.03
40
56.2
33.8
0.5
0.89
2.40
50
58.8
31.2
0.5
0.85
1.32
30
48
42
1.0
2.08
15.85
40
50.8
39.2
0.5
0.98
8.32
50
57
33
0.0
0.88
1.99
30
45.2
44.8
0.5
1.11
30.20
40
48.2
41.8
0.5
1.04
15.14
50
53.8
36.2
0.5
0.93
4.17
30
43.2
46.8
0.5
1.16
47.86
40
45.2
44.8
0.5
1.11
30.20
50
48.2
41.8
0.5
1.04
15.14
Table 4: Processed Data with Uncertainties and Absorption Coefficient
15
Material Thickness (mm) vs Sound Level (dB)
70
Distance of material from source
30cm
Sound Level (dB)
60
Distance of material from source
40cm
50
Distance of material from source
50cm
40
30
y = -22.908x + 64.516
R² = 0.9907
20
y = -23.651x + 60.711
R² = 0.9066
10
0
0
0.2
0.4
0.6
Material Thickness (mm)
0.8
y = -22.642x + 57.538
R² = 0.8840
Graph 1: Relation between Material Thickness (mm) and Sound Level (dB)
In the above graph, one can observe that there is a negative correlation between the thickness
of the material and the transmitted sound level. From the graph, as the thickness of the
material is increased, there is a gradual decrease in the sound level that is being transmitted at
the end of the experiment.
-
The line of best fit for the line 30cm has an R-squared value of 0.9907 which
precisely shows that the graph is in a linear proportion to each other. The equation of
this line is 𝑦 = −22.908𝑥 + 64.516. From this equation, we can observe that the
gradient is −22.908, which proves that an increase in 0.1mm of material thickness
will decrease 22.908dB of transmitted sound level.
-
The line of best fit for the line 40cm has an R-squared value of 0.9066. This value is
slightly lower that the value 0.91 (which is the lower limit for a perfect correlation)
and depicts that even though there is a linear correlation between the values, there is a
slight decrease in the relationship. This effect of reduced correlation could be due to
the escape of sound waves through the pipe.
16
-
The line of best fit for the line 50cm has an R-squared value of 0.8840 which
demonstrates that the linear correlation between material thickness and transmitted
sound level has gradually decreased with an increase in the distance of the material
from the source.
Material Thickness (mm) vs Absorption Coefficient (10-6)
Absorption Coefficient (10-6)
60
50
Distance of material from source
30cm
40
Distance of material from source
40cm
30
Distance of material from source
50cm
20
y = 79.683x - 9.1129
R² = 0.9753
10
y = 49.327x - 6.809
R² = 0.9422
0
0
-10
0.2
0.4
0.6
0.8
y = 23.333x - 3.9954
R² = 0.8181
Material Thickness (mm)
Graph 2: Relation between Material Thickness (mm) and Absorption Coefficient (10^-6)
In the graph above, we can notice that there is a positive correlation between absorption
coefficient and the material thickness. This justifies the stated hypothesis that as the material
thickness increases, there is a gradual increase in the absorption coefficient of the material
(aluminum sheets).
-
The line of best fit for the line 30cm has an R-squared value of 0.9753 with the line
equation 𝑦 = 23.333𝑥 − 3.9954. The r-squared value justifies that there is a high
positive correlation for the distance of material 30cm from the source. The line
equation shows us that for every 1mm increase in material thickness, 23.333 × 10−6
of the absorption coefficient increases and is inversely proportional to the transmitted
sound level.
17
-
The line of best fit for the line 40cm has an R-squared value of 0.9422 with the line
equation 𝑦 = 49.327𝑥 − 6.809. The r-squared value for this line of best fit shows
that the correlation between both the variables exists in positive form. The line
equations states that for every 1mm increase in material thickness, there is an increase
of 49.327 × 10−6 of absorption coefficient.
-
The line of best fit for the line 50cm has an R-squared value of 0.8181 with the line
equation 𝑦 = 23.333𝑥 − 3.9954. The r-squared value of this line of best fit exhibits a
lowered positive correlation between the two variables. The line equation states that
for every 1mm increase in material thickness, there is an increase of 23.333 × 10−6
of absorption coefficient.
4. Conclusion
This investigation was initially conducted to explore the relationship between the material
thickness and its effect on the transmitted sound level while passing in an impedance tube.
While working on the same, several compelling conclusions were made.
The original methodology used for this investigation contained the construction of an
impedance tube which consists of 2 microphones (one for reflection and the other for
incident). But usage of the same methodology was considered inappropriate for this
investigation. Instead, the methodology was tweaked to suit the transmission of sound waves
with the help of only one sensor and a material of specified thickness at the specified distance
from the source.
Subsequent to the experimentation, the results found involved the values in decibels. With the
help of the derived equation (4), the raw data could then be processed to get the sound
absorption coefficient. Forthwith, the processed data (absorption coefficient) was then plotted
with material thickness to find out the effect of material thickness on the absorption
18
coefficient. From graph 2, we can observe that the material thickness and absorption
coefficient have a positive correlation and that they are directly proportional to each other.
Since the average r-square value for all the three distances (30cm, 40cm, 50cm) add up to
approximately 0.906, the final correlation is considered to be a positive relationship between
material thickness and absorption coefficient.
The uncertainties found in this investigation are mostly 0.5dB for the raw data and are
extremely low as the entire experiment was conducted using SPARKvue software which
accurately definite sensor. According to the software, the uncertainty in the data collected is
extremely low as the sensor obtained the data in tabular form and in graphical form.
In conclusion, with the results acquired from the software and the processed data, the graphs
outlined provide evidence that the experimental hypothesis stated in this investigation is
valid. With the help of this investigation, I was able to validate that “the material thickness
of aluminum sheets has an impact on the sound level that is transmitted through the
material in an impedance tube by calculating absorption coefficient of the material.”
5. Evaluation
5.1 Limitations
-
One of the biggest limitations for this investigation is the range from which the sound
level (dB) was detected by the sensor. The PASCO PASPort sensor had a range from
40dB to 90dB with 40dB as the lowest detectable background noise. As the material
thickness increased, the sound level detected by the sensor on the other end of the
tube was lowering at a high pace. This was the reason the variable of material
thickness could not be taken for more than 0.7mm thickness. When the thickness of
0.8mm was taken, the transmitted sound level almost blended in with the lowest
detectable noise (40dB).
19
-
Another limitation of this investigation is the escaping of sound through the masking
tape used to connect two pipes with material between them. Since PVC pipes were
used to conduct the experiment, the pipes could not be welded together with
aluminum sheets between them as they were made of low carbon plastic and not steel.
When the sound of frequency 2000Hz was sent through the pipe of length 100cm and
with no material in between, the sound level reached 90dB but was comparatively low
when the pipe was cut and stuck with tape in between. This may have caused the
minor differences in the accuracy of the data that was collected using the sensor with
pipes of different lengths and aluminum sheets of different thicknesses.
5.2 Improvements
Since this investigation determines the sound level on the other side of the material with
specified thickness, the experiment could also be improved as per the following:
-
Since the experiments conducted in this investigation had a sound level limit from
40dB to 90dB, using a stronger sensor for the detection of transmitted sound level
could have improved the results of the experiment.
-
The sound source for these experiments was a single Bluetooth earphone which
produced the sound of frequency 2000Hz at an equivalently low loudness when
compared to a loudspeaker used for heavy experimentation. Using a bigger radius
pipe with louder sound source could increase the sound level produced and hence the
sound waves transmitted to the other side. Doing this will provide better results to
analyze and conclude the hypothesis from the research question with better graphs
and data.
20
5.3 Extensions
This investigation could also be extended with certain other variables such as:
-
For the experiments in this investigation, aluminum sheets were used as the main
material. Other acoustic materials23 such as polyurethane foam (thermocol),
fiberglass, rock wool, acoustic foams could also be used to inquire about the sound
absorption capacity of varied materials instead of a single one.
-
Rather than altering the thicknesses of a solid object (aluminum sheets), the
experiments could also be conducted for different media24 such as solid, liquid or
even gas. Regulating this investigation with different media will explain and compare
the transmission of sound waves through different media.
-
If the medium of liquid can be taken in the place of solids, the density 25 of the liquid
can be amended to determine the effect of density of a liquid on the transmission of
sound waves through them.
-
Air gap thickness26 can be another development to the experiment. Since the sound
due to the reflection from the material has been omitted in this experiment, with the
help of a setup consisting of two microphones, and the change in the air gap thickness
between material and back-plate can also be considered as an extension to determine
its relation with transmitted sound level.
23
Cucharero, Jose. "Influence of Sound-Absorbing Material Placement on Room Acoustical Parameters." MDPI
- Publisher of Open Access Journals, MDPI, www.mdpi.com/2624-599X/1/3/38/pdf. Accessed 16 Nov. 2021.
24
Seddeq, Hoda S. "Factors Influencing Acoustic Performance of Sound Absorptive Materials." CiteSeerX1,
AJBAS, citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1039.7353&rep=rep1&type=pdf. Accessed
9 Dec. 2021.
25
Nandanwar, Anand. "Influence of Density on Sound Absorption Coefficient of Fibre Board." SCIRP Open
Access, 26 Jan. 2017, www.scirp.org/journal/paperinformation.aspx?paperid=73876. Accessed 29 Nov. 2021.
26
Mvubu, Mlando B., et al. "Effects of air gap, fibre type and blend ratio on sound absorption performance of
needle-punched non-woven fabrics." Sage Journals,
journals.sagepub.com/doi/full/10.1177/1558925019840874. Accessed 11 Nov. 2021.
21
6. Bibliography
"Acoustics 101 - Learn About Acoustics." Acoustical Surfaces, 28 July 2014,
www.acousticalsurfaces.com/acoustic_IOI/101home.htm. Accessed 14 Nov. 2021.
Biezen, Michel V. "Physics - Mechanics: Sound and Sound Waves (9 of 47) Decibel Scale
Conversion." YouTube, 7 Oct. 2013, www.youtu.be/h5HIsz1RmH8. Accessed 11
Nov. 2021.
"Decibel Dropp & Noise Reduction Coefficients for Material Combinations." Thermaxx
Blog: Insulation, Energy Savings, & More, 21 Oct. 2021,
www.blog.thermaxxjackets.com/decibel-drop-noise-reduction-coefficients-formaterial-combinations. Accessed 29 Oct. 2021.
Gregersen, Erik. "Decibel | Definition, Formula, & Facts." Encyclopedia Britannica,
17 Jan. 2018, www.britannica.com/science/decibel.
"Intensity and Distance – Understanding Sound." Understanding Sound – Simple Book
Publishing, www.sound.pressbooks.com/chapter/intensity-and-distance-april-2019version/. Accessed 15 Nov. 2021.
Lamancusa, J. S. "TRANSMISSION OF SOUND THROUGH STRUCTURES." Penn State
Engineering: Mechanical and Nuclear Engineering Department Split, Penn State Noise Control, 12 Jan. 2000, www.mne.psu.edu/lamancusa/me458/9_trans.pdf.
Accessed 27 Oct. 2021.
"Physics Tutorial: Intensity and the Decibel Scale." The Physics Classroom,
www.physicsclassroom.com/class/sound/Lesson-2/Intensity-and-the-Decibel-Scale.
Accessed 13 Nov. 2021.
Robin, Olivier, et al. "Measurement of the Absorption Coefficient of Sound Absorbing
Materials Under a Synthesized Diffuse Acoustic Field." Scitation: Acoustical Society
22
of America, ASA: The Journal of the Acoustical Society of America, 16 June 2014,
www.asa.scitation.org/doi/10.1121/1.4881321. Accessed 3 Dec. 2021.
"Sound - Room Absorption Coefficients." Engineering ToolBox,
www.engineeringtoolbox.com/accoustic-sound-absorption-d_68.html. Accessed 08
Nov. 2021.
"Sound Absorption and Sound Insulation." Hem | Avdelningen För Teknisk Akustik,
www.akustik.lth.se/fileadmin/tekniskakustik/education/Acoustics/Lecture_Sound_A
bsorption_Insulation.pdf. Accessed 02 Nov. 2021.
"Sound Absorption Coefficient." ScienceDirect.com | Science, Health and Medical Journals,
Full Text Articles and Books, www.sciencedirect.com/topics/engineering/soundabsorption-coefficient. Accessed 17 Oct. 2021.
"Sound Intensity Formula." BYJUS, 9 July 2019, byjus.com/sound-intensity-formula/.
"The Sound Level at a Distance of 3.00 M from a Source is 120 DB. At What Distance Will
the Sound Level Be (a) 100 DB and (b) 10.0 DB?" Doubtnut, 29 Apr. 2020,
www.doubtnut.com/question-answer-physics/the-sound-level-at-a-distance-of-300m-from-a-source-is-120-db-at-what-distance-will-the-sound-level-11393439.
Accessed 20 Oct. 2021.
"Sound Transmission." Encyclopedia.com | Free Online Encyclopedia,
www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-andmaps/sound-transmission. Accessed 11 Oct. 2021.
Suhanek, Mia. "(PDF) Student Project of Building an Impedance Tube." ResearchGate,
1 June 2008,
www.researchgate.net/publication/5325257_Student_project_of_building_an_imped
ance_tube. Accessed 19 Oct. 2021.
23
7. Appendices
1. Graphs generated by SPARKvue Software:
-
30cm
o 0.1mm thickness
o 0.25mm thickness
24
o 0.3mm thickness
o 0.5mm thickness
25
o 0.7mm thickness
-
Comparison graph between all the thicknesses at 30cm distance
26
-
40cm
o 0.1mm thickness
o 0.25mm thickness
27
o 0.3mm thickness
o 0.5mm thickness
28
o 0.7mm thickness
-
Comparison graph between all the thicknesses at 40cm distance
29
-
50cm
o 0.1mm thickness
-
0.25mm thickness
30
o 0.3mm thickness
o 0.5mm thickness
31
o 0.7mm thickness
-
Comparison graph between all the thicknesses at 50cm distance
32