The Effect of Different Steel Structures on the Signal Strength of Radio Waves

Thanvir Ahmed and Nafis Jaigirdar

Macomb Mathematics Science Technology Center

Advanced Placement Physics

12 B

Mr. McMillan / Mrs. Cybulski / Mr. Acre / Mrs. Dewey

17 December 2015

The Effect of Different Steel Structures on the Signal Strength of Radio Waves

This experiment was conducted in order to research six different structural designs

and the effect that they would have upon the signal strength of a Samsung Galaxy S6 cell

phone. This was done because different structural designs have different effects on

electromagnetic waves. The different structural designs that were tested within this

experiment were: Solid Plate, Bubbled Plate, Striped Plate, Concave-Up Plate, Concave-

Down Plate, and a Base Plate. The response variable, or the dependent variable was the

signal strength of cell phone (dBm), this is the strength of the radio waves that reach the cell

phone. This research demonstrates which structures should be implemented in certain

scenarios, such as military bunkers preventing radio waves, or satellite dishes utilizing radio

waves.

This was done by placing the cell phone within a steel box, and then placing the

structure (the plate) being tested on top of the box. The cell phone had a preloaded

application to measure the signal strength which was launched prior to placing the phone

within the box. The signal strength of the phone was then recorded. The hypothesis stating

that the Concave Down Plate would cause the most amount of signal interference, and that

Concave Up Plate would cause the least amount of interference was accepted. This is based

on the results of the ANOVA test and the two-sample t tests. The t tests concluded that only

the Bubble Plate and the Striped Plate produced the same amount of interference. Box plots

and visual analysis concluded that the Concave Up Plate caused the least amount of

interference, and the Concave Down Plate caused the most.

Table of Contents

Introduction............................................................................................................................1

Review of Literature..............................................................................................................3

Problem Statement.................................................................................................................8

Experimental Design..............................................................................................................9

Data and Observations...........................................................................................................13

Data Analysis and Interpretation...........................................................................................16

Conclusion.............................................................................................................................22

Appendix A: Constructing Plates...........................................................................................27

Appendix B: Formulas and Sample Calculations..................................................................29

Appendix C: Professional Contact Conversation..................................................................32

Works Cited...........................................................................................................................40

Introduction

Communication is a vital part of human civilization. Communication serves as a

means to spread information, expanding knowledge beyond horizons never before imagined.

Today, the most used device is a cellular phone with 90% of adults in the United States

using a cell phone (Livingston). With the press of a couple of buttons, cell phones are able

connect people to the entire world. This connectivity, however, depends entirely on radio

waves. Cell phones operate and transmit data via electromagnetic waves with a frequency of

about 1900 MHz, known as radio waves. Interference of these radio waves can be caused by

many different factors. The wave can be reflected off of the surface of the material, refracted

through the material, or absorbed (partially or completely) by the material. This interference

inevitably decreases the signal strength of the radio waves being transmitted to and from the

phone. Lower signal strength results in poor reception and makes communication via cell

phone difficult, if not impossible.

There are numerous factors that can affect the signal strength of radio waves. An

electromagnetic wave can be altered by being reflected off of the surface of the material,

refracted through the material, or absorbed (partially or completely) by the material. All of

these interactions with matter can alter signal strength, which ranges from -130 dBm to -60

dBm, -60 dBm being excellent signal, and -130 dBm being terrible signal. The factor with

the most profound effect upon the signal strength is the propagation of the wave. The

propagation of a wave refers to the direction in which it travels forward at the speed of light.

It is a commonly observed occurrence that cell phone signal is lost when traveling through a

tunnel or entering a very large building. This is due to the fact that the propagation of the

radio waves is altered through diffraction, absorption, and reflection. The radio waves are

absorbed by the tunnel walls and spread out as a result of diffraction. Diffraction is the

bending of electromagnetic waves due to structural blocks. Different structural designs have

different effects upon the propagation of radio waves, ultimately having an effect on the

signal strength.

This experiment was conducted in order to research six different structural designs

and the effect that they would have upon the signal strength of a Samsung Galaxy S6 cell

phone. This was done because different structural designs have different effects on

electromagnetic waves. The different structural designs that were tested within this

experiment were: Solid Plate, Bubbled Plate, Striped Plate, Concave-Up Plate, and

Concave-Down Plate, as well as a Base Plate. The Base Plate had no plate causing

interference and served as a control for comparison. These different plates represent

different structural designs within the real world such as steel lined building, tunnels,

bunkers, and even satellite dishes. The response variable, or the dependent variable was the

signal strength of cell phone (dBm), which is the strength of the radio waves that reach the

cell phone.

Being able to determine the effect of different structural designs upon the signal

strength of radio waves would allow for certain structures to be implemented in certain

scenarios. For example, a military level bunker would want to minimize the amount of radio

waves being transmitted in and out of the building for security purposes. The most effective

way to do this would be to design the bunker in a specific way to interfere with the radio

waves. An architect who knows what structural design interferes with radio waves the most

would be able to design such a building.

Review of Literature

Cell phones are a vital part of daily life. Modern day smartphones can do just about

anything; however, they are limited by the range of their signals. Wireless communications

are constricted to a small portion of the electromagnetic spectrum. Cell phones, like other

forms of wireless communication, transfer information through radio waves, a form of

electromagnetic radiation. Radio waves have the characteristics of any other electromagnetic

wave, they have wavelengths and frequencies, but more importantly they interact with

matter. An electromagnetic wave can interact with matter in four different ways. The wave

can be reflected off of the surface of the material, refracted through the material, diffracted

off of the surface, or absorbed (partially or completely) by the material. All four of these

interactions cause interference with the path of the wave, and change the direction of the

wave (How Electromagnetic Radiation Interacts With Matter). Today, most buildings,

tunnels, or any other structures most likely have steel foundations. These structures interfere

with the transmission of radio waves by altering the propagation of radio waves. The goal of

this experiment was to uncover the effect of different structural designs so that the

interference of these structures upon radio waves can be minimized.

Most forms of wireless communication are transmitted through electromagnetic

waves such as radio waves. Radio waves have the longest wavelengths of all the

electromagnetic waves, and also have the lowest frequencies (Netting). The most common

form of wireless communication is cell phone use. Cell phones have a cell receiver and a

transmitter. These are both used to communicate information between the cell phone and the

cell tower that is emitting a radio wave to the cell phone. The frequencies of radio waves

range from 3 kilohertz (kHz) to 300 gigahertz (GHz). Most cell phones operate with

frequencies of either of 800 or 1900 Megahertz (MHz) (Lucas). Originally, radio waves

scrambled and interfered with other radio waves. If two stations were sending a radio signal

at the same frequency, then they would interfere with each other. This is no longer the case,

as most radio frequencies have their own purpose, specific radio channels have their own

frequencies. Radio frequencies also experience interference from different structures and

materials, such as steel and concrete. This is why cell phone reception is weak within

tunnels (Adam). Within this experiment, a cell phone operating at 1900 MHz was used, and

different steel structures were tested.

Radio waves do not require a medium to travel through because they are

electromagnetic waves. Matter can cause an interference with the propagation of radio

waves. The propagation of radio waves can be affected significantly by interference from

matter or other waves, and by reflection off of surfaces (Communications System). A

lustrous, or shiny, surface can change the path of a radio wave. Propagation refers to the

behavior of radio waves, from one point to another (Meisels). Diffraction is the bending of

electromagnetic waves due to structural blocks. In her experiment Regina Meisels, a

researcher for the Austrian Science Organization, tested the propagation levels of

electromagnetic waves when aimed and sent through different rock structures. In her

findings Meisels concluded that the rock type played a pivotal role in the strength of the

waves that transferred through, concluding that some of the waves were diffracted and some

were absorbed. Meisels used smooth surfaced rocks and rocks with a curved and a rough

surface in her experiment. These variations in strength can be attributed to a wide variety of

factors ranged from the amount of waves propagated to the amount absorbed by the rocks

themselves. Meisels used smooth curved rocks, and found that they allowed for stronger

signals. The trials that she ran with more rectangular rocks produced weaker signals.

Similarly, satellite dishes are shaped upwards at a curve, while tunnels are shaped

downwards at a curve.

Signal strength of cell phones is dependent upon the strength of the radio waves

emitted to and from them. Modern day smartphones can record the strength of the radio

waves, and users can view these records by downloading certain applications. The signal

strength of a cell phone is measured in decibel-milliwatts (dBm), or the power ratio in

decibels (dB) of the measured power referenced to one milliwatt (mW). This ranges from -

130 dBm to -60 dBm (Livingston). The signal strength of -130 dBm would result in no

signal, while the signal strength of -60dBm would result in excellent signal. The signal

strength of -130 dBm is nearly impossible to achieve, before conducting this experiment a

Faraday Cage was replicated to get a reading with no signal. “The point of a Faraday Cage

is to see if you measure zero when you should. It is done all the time in science to make sure

you are not getting fooled by false signals.” (Cinabro). Mr. Cinabro was contacted for his

extensive knowledge within the field of radio waves, a copy of this conversation is shown in

Appendix C. This works by surrounding a receiver, such as a cell phone, and preventing any

radio waves from reaching the phone. Likewise, these signal strengths will vary in different

conditions. For example, if the cell phone is outside with nothing interfering with the radio

wave transmission and if it is fairly close to a cell tower, the signal strength would be closer

to -60 dBm than -130dBm. However, if the cell phone is put inside of a building then the

interference from that building will cause the signal strength to lean more towards -130

dBm.

Another example of how electromagnetic propagation can be manipulated was

demonstrated by Chang-Fu Yang, Professor at the Taiwan Institute of Technology. In his

experiment Yang used ray tubing to propagate light particles in order to identify the path

that individual particles travel during propagation (Yang). A ray tube is a vacuum tube that

moves an electric beam back and forth. Although Yang’s experiment used light waves

similar results can be expected from radio waves. Based on the research conducted by both

Yang and Meisels it can be said that the two main reasons signal strengths are weaker after

traveling through objects are because of the absorption of the waves by different materials

and propagation.

The temperature of the medium is also another important factor in the penetration

ability of waves. It was found that lower temperatures reflect less of the waves (Hashimoto

et al). This was a study led by Hashimoto, a professor at the Tokyo National University. In

his experiment. Hashimoto and his peers tried to identify how a wave would propagate at

different temperatures. They concluded that at higher temperatures the particles which made

up the medium were moving faster, adding more space between each of the particles, and

allowing the electromagnetic waves to travel through. To avoid an error, precautions were

taken to maintain constant temperatures when heating or cooling a structure. The

temperature of the structures remained consistent throughout the trials to ensure accurate

data collection. This experiment was conducted within a vehicle that was parked

approximately 10ft away from a cell phone tower.

Another experiment was conducted at The Institution of Electrical Engineers by an

engineer known as Feodora Berz. Berz tested microwaves to identify the effect of

diffraction on the power of the wave. The power difference between the outermost rays and

the innermost rays was about 0.05% (Berz). The innermost rays were the stronger of the

two. Likewise, it is important to note that the placement of structures can change the amount

of signals that penetrate through. Diffraction of the radio waves alters the signal strength of

the wave because it spreads some of the wave across a surface. For the purpose of this

experiment precautions were taken to ensure that the structures always blocked the signal in

the same path, minimizing the fluctuations within the signal strength, which in turn

produced more accurate data.

Elevation also plays a critical role in the strength of radio wave signals. On average,

as the floor level of the building increases the overall signal quality of cell phones decreases

(Walker). This is due to atmospheric changes and conditions, and also the distance from a

cell tower increases with height. This means that the elevation at which the radio waves are

being tested must be kept constant. Overall, many precautions were taken based on the

research of Hashimoto, Berz, and Walker to avoid errors within the experimental design.

This included keeping the temperature of the structure, elevation of the transmitter/receiver,

and layout of the structures constant.

Wireless communication utilizes radio waves in order to share information. A

common use for radio waves is cell phones. An electromagnetic wave can be altered by

being reflected off of the surface of the material, refracted through the material, or absorbed

by the material. All of these interactions with matter can alter signal strength, which ranges

from -130 dBm to -60 dBm. The temperature, the elevation, and the layout of the structure

can also affect the signal strength, thus they should be kept constant when testing for the

signal strength of radio waves.

Problem Statement

Problem Statement:

How do different steel structural designs (Solid Plate, Bubbled Plate, Striped Plate,

Concave-Up Plate, and Concave-Down Plate) affect the propagation of electromagnetic

waves?

Hypothesis:

If different steel structural designs are used to cause interference with the

transmission of radio waves, then the Concave-Up Plate will produce the least amount of

interference.

Data Measured:

There was one independent variable and one dependent variable within this

experiment. The steel structural designs were held as the explanatory variable, or

independent variable. The different types of steel structures were Solid Plate, Bubbled Plate,

Striped Plate, Concave-Up Plate, and Concave-Down Plate. All of these plates had the same

surface area to eliminate any unwanted interference. The response variable, or the dependent

variable was the signal strength of cell phone (dBm), which is the strength of the radio

waves that reach the cell phone. There were 30 trials conducted for each plate. The order

that the trials were conducted was randomized in order to eliminate any bias. The signal

strength of the radio waves was measured without any interference as base to compare all

other trials to. A One-way Analysis of Variance (ANOVA) was conducted in order to

compare the means of all of the structures and determine if the different steel structures had

a significant effect upon the signal strength of radio waves

Experimental Design

Materials:

Samsung Galaxy S6 Cell Phone Network Signal Info AppSteel Curved Plate 7” X 7” Wiss 7” Metal Shear Scissors (4) Steel Plate Vertical Slits 1.75” X 7” Ti – Nspire CX Calculator Steel Solid Plate 7” X 7” Twist-It Ruler Steel Bubbled Plate 7” x 7”SentrySafe 7” X 7” Steel Box

Procedures:

1. Construct the plates required for the experiment. Instructions on how to cut these plates can be found in Appendix A.

2. Randomize the orders in which trials should be conducted by using the random integer function on the Ti – Nspire CX Calculator. There are 30 trials per plate, meaning 180 trials in total. These trials were grouped together and then randomized. This is done by grouping every 5 trials together, such that there are 36 groups. The order of these groups was then randomized with the random integer function.

3. Place the phone inside the center of the steel box. The phone should not move from this position until the trial is completed.

4. Launch the Network Signal Info App and then place the steel plate that correlates with the trial on top of the steel box, in order to cause interference with the signal strength of the cell phone.

5. For the trials using the Base Plate, there should be nothing placed on or in the box except for the cell phone.

6. For the Bubble Plate, place the plate on top of the box, such that the entire face of the box is covered.

7. For the Solid Plate, place the plate on top of the box, such that the entire face of the box is covered.

8. For the trials using the Concave Up Plate, the plate should be placed within the box in order to maximize the interference with the signal strength.

9. For the trails using the Concave Down Plate, the plate should be placed within the box in order to maximize the interference with the signal strength.

10. For the trails using the steel slits, the slits should be placed on top of the box, in a manner in which they fully cover the top of the box.

11. Wait approximately 1 minute for the Network Signal Info App to render, and then lift the steel plate up.

12. Record the signal strength of the cell phone that is shown on the application (this is an average).

13. Repeat steps 2 through 12 for all of the trials. Analyze the data using a One Way Analysis of Variance (ANOVA Test) and two-sample t Tests accordingly.

Diagrams:

Figure 1. Materials

Figure 1 shows the materials that were used throughout this experiment. It is

important to note that the steel plates were all positioned on top of the box and covered the

top completely in order to prevent any unnecessary propagation, and to maximize the

interference that the cell phone signals undergo. The materials that were unique to this

experiment were the different steel plates, the steel box, and the Samsung Galaxy S6.

Steel Curved Plate Steel Solid Plate Steel Bubbled Plate

Metal Shears Steel Plate Slits Ti – Nspire CX Calculator

Twist-It Ruler Calculator

Steel Box Calculator

Galaxy S6

Figure 2 shows the setup of the box. The cell phone was positioned inside the box

and directly under the steel plates. As shown, the steel plates were placed on top of the box

and made stable using the rim of the box, and the Network Signal Info App was running on

the phone. The trial shown in this figure is one which used steel strips. It is important to note

that in this figure two of the strips were removed to demonstrate how the phone was placed

in the box.

Figure 2. Box Setup

Steel Box Calculator

Steel Plate Slits

Galaxy S6

Figure 3. Network Signal Info App

Figure 3 is a screenshot of the data collected by the phone. The main focus of this

figure is signal strength of the cell phone, measured in decibel-milliwatts (dBm). Note that

the closer the dBm is to zero the better the signal strength of the phone. This was a trial with

no plate, and the signal strength is about -78 dBm, which is a very strong signal strength. It

takes approximately one minute for the application to get an accurate reading.

Data and Observations

Table 1Data Table

TrialBase

(dBm)Concave Up

(dBm)Striped(dBm)

Bubbled(dBm)

Solid(dBm)

Concave Down(dBm)

1 -76 -80 -86 -88 -94 -1032 -78 -81 -85 -85 -95 -1053 -77 -79 -87 -86 -95 -1034 -80 -82 -86 -85 -93 -1055 -78 -78 -86 -87 -92 -1066 -79 -80 -85 -88 -94 -1027 -77 -80 -86 -89 -92 -1058 -78 -77 -88 -87 -95 -1039 -76 -83 -87 -86 -94 -105

10 -81 -80 -86 -86 -96 -10311 -75 -80 -88 -87 -91 -10312 -76 -81 -86 -86 -94 -10613 -77 -82 -87 -86 -94 -10314 -78 -78 -86 -85 -95 -10515 -78 -79 -86 -85 -96 -10616 -79 -80 -85 -89 -93 -10417 -76 -80 -86 -87 -92 -10618 -81 -78 -85 -85 -92 -10519 -75 -83 -87 -86 -95 -10120 -77 -82 -88 -89 -94 -10621 -78 -77 -86 -86 -96 -10122 -79 -80 -85 -88 -93 -10623 -78 -80 -87 -89 -91 -10424 -79 -80 -86 -87 -95 -10525 -79 -78 -88 -86 -94 -10326 -76 -81 -85 -87 -93 -10227 -81 -79 -86 -86 -94 -10428 -78 -80 -88 -89 -94 -10429 -79 -82 -87 -87 -94 -10230 -79 -79 -86 -85 -96 -106

Average: -77.93 -79.97 -86.33 -86.73 -93.87 -104.07

Table 1 shows all of the data that was collected within this experiment. The lowest

average signal strength is affiliated with that of the Concave Down Plate. The highest

average signal strength was produced by the Base Plate, or the trials that had no plate. The

highest signal strength produced by a plate was by the Concave Up Plate. A box plot of this

data is shown in Figure 5.

Table 2Observations Table Trial Type Observation

18 Base The metal box was accidently closed shut before trial began then reopened, trial was restarted.

27 Base The metal box was accidently closed shut before trial began then reopened, trial was restarted.

19 Concave up Plate fell into the box however trial was reset and run again.20 Concave up Plate fell into the box however trial was reset and run again.29 Concave up Plate fell into the box however trial was reset and run again.

19 Concave down

Plate was slightly off center, trial was restarted.

22 Concave down

Waited for more than 1 minute, trial was restarted.

2 Striped Striped were placed with a larger gap, trial was run again.

28 Striped Striped were too close to one another, spread out, and trial was run again.

7 Bubbled Wrong side of plate was placed over box, trial was run again.20 Bubbled Wrong side of plate was placed over box, trial was run again.11 Solid Trial concluded before 1 minute, trial was run again. 23 Solid Plate was slightly off center, trial was restarted.

Table 2 shows the observations that were made for specific plates and the trial

number that correlates with them. The observations mainly include trials that were done

incorrectly, and had to be redone. The Bubbled Plate has two different sides, the side that

was placed up was the side in which the holes were drilled. Trials that were conducted with

the drilled face down were redone. The phone was placed within the box and the trials lasted

approximately one minute. Trials that lasted longer than a minute or less than a minute were

redone as well. The plates were poorly placed for some trials; these were also redone.

Figure 4 shows the setup of the box. The cell phone was positioned inside the box

and directly under the steel plates. As shown, the steel plates were placed on top of the box

and made stable using the rim of the box, and the Network Signal Info App was running on

the phone. The trial shown in this figure is one which used steel strips. It is important to note

that in this figure two of the strips were removed to demonstrate how the Samsung Galaxy

S6 cell phone was placed in the box. The image on the right shows that the cellphone

without any plates. This was a Base Plate trial, or a control. There were plates placed on this

in order to cause interference.

Data Analysis and Interpretation

Figure 4. Box Setup Before and After

Steel Box Calculator

Steel Plate Slits

Galaxy S6

The data that was collected must be analyzed to determine which of the steel plates

had the greatest effect upon the signal strength and which one had the least effect. There

were 30 trials for each individual plate, such that there were 180 trials in total. The order of

said trials was randomized with a Ti-Nspire calculator. This was done by grouping every 5

trials together, such that there were 36 groups. The order of these groups was then

randomized. This helps make the results valid, as randomization reduces bias. Each trial was

conducted independently, meaning the results of the trials did not affect each other. A One-

way Analysis of Variance (ANOVA) was conducted in order to compare the means of all of

the structures and determine if the different steel structures had a significant effect upon the

signal strength of radio waves. Two-sample t tests were then used to further analyze the data

by comparing the means of two independent samples. These were the appropriate tests to

use because there were six independent samples within this experiment: The Solid Plate,

Bubbled Plate, Striped Plate, Concave-Up Plate, Concave-Down Plate, and the Base (which

did not use a plate). These different plates were being tested to determine which one had the

greatest effect upon the signal strength of radio waves and which one had the least. An

ANOVA test compares all of the samples, the plates, to one another in order to determine

whether or not the effect on the signal strength was equal for all of the plates. There were

some overlaps within the box plot of the data collected from individual plates.

Consequently, Two-sample t tests were utilized to determine whether or not the effect on the

signal strength was equal for two different plates. Refer to Appendix B for sample

calculations of these tests.

-81

-79-78 -77

-75

Figure 5. Box Plots of Signal Strengths

Figure 5 is a box plot that illustrates the data that was collected in decibel-milliwatts

(dBm). The data is fairly normal, and there are not outliers. The medians of the individual

box plots are relatively close to their means, further indicating that the data is symmetric.

There are mean lines for each data set, which are indicated with a long vertical line on the

boxplots. It is important to note that the striped and the bubbled data have a significant

overlap. All of the data for the Striped Plate falls within the top 75% of the data for the

bubbled data. Consequently, a two-sample t test was conducted in order to identify if the

data between the two structures were in fact equal. The same was done for the data from the

Base and Concave Up Plates, as there is a noticeable overlap between these two data sets.

The Concave Down Plate had the greatest effect on the signal strength, as that data is the

farthest away from the Base Plate data.

Key

Base

Concave Up

Striped

Bubbled

Solid

Concave Down

1

-106-105

-104-103

-101

-96

-95 -94 -93

-91

-89

-88-86.5

-86

-85

-88

-87 -86

-85

-83

-81 -80 -79

-77

Signal Strength (dBm)

The box plot indicates that the different plates had different effects on the signal

strength, but an ANOVA test was still conducted in order to prove this statistically

significant. Before conducting an ANOVA test, there are certain assumptions that must be

met. The assumptions for an ANOVA test include independence of each case and the data to

come from a normal population. The standard deviations of the different plates are also very

close, indicating that the variances are equal. The trials were conducted separately and

independent of one another. The Central Limit Theorem states that the sampling distribution

of the sampling means approaches a normal distribution as the sample size gets larger, the

sample size for each plate is 30 trials, so this supports the claim of normality. The rule of

thumb for normality is that the largest standard deviation is not more than two times the

smallest standard deviation. The largest standard deviation was the Concave Up Plate with

1.61 dBm. The smallest was 0.99 dBm, with the Striped Plate. Since this meets the rule of

thumb, the data was assumed normal. There were no outliers within any of the box plots. All

of the assumptions were met for the ANOVA test, meaning that testing could proceed. The

hypothesis for the ANOVA compares the mean values from each of the different structures.

H o : μ1=μ2=μ3=μ4=μ5=μ6

H a : Not all of μ1=μ2=μ3=μ4=μ5=μ6

The null hypothesis states that the mean signal strengths for all structures are the same. The

alternative hypothesis states that the mean signal strengths for all structures are not all the

same. The ANOVA test was conducted with this hypothesis. The alpha level for this test

was 0.05, this is the level where the null hypothesis is either rejected or is failed to be

rejected.

Figure 6. One Way Analysis of Variance Test (ANOVA)

Figure 6 contains the results of the one way ANOVA test. The p-value is essentially

zero (5.0∗10−136). Consequently, the null hypothesis was rejected at an alpha level of 0.05.

This indicates that all of the trials do not produce the same signal strength. This also means

that there is approximately a 0% chance of getting results this extreme by chance alone if

the null hypothesis is true.

The results from the ANOVA test indicate that the signal strengths of the different

plates were not all equal; the plates produced different signal strengths. However, the data of

some plates overlapped with the data of other plates. These overlapping plates needed to be

tested in order to conclude whether or not the signal strength produced was equal between

them. To compare the data of two independent samples, a two-sample t test was conducted.

A two-sample t test compares the mean of two independent samples. There are certain

assumptions that must be met in order to conduct this test. The assumptions for two-sample

t test include independence of both cases, the data comes from a normally distributed

population, and equal standard deviations. As stated above that trials were independent of

one another. All of the assumptions were met for the two-sample t test, and the test was

conducted.

H o : μn 1=μn 2

H a : μn 1≠ μn 2

The null hypothesis states that the mean signal strengths for both structures are the same.

The alternative hypothesis states that the signal strengths for both structures are not the

same. This was the hypothesis that was used for both two-sample t tests below. The alpha

level for this test was 0.05. The data produced by the Bubble Plate overlapped with that of

the Striped Plate, the two-sample t test conducted in order to test is shown in Figure 7. The

data produced by the Base Plate overlapped with that of the Concave Up Plate, the two-

sample t test conducted in order to test this is shown in Figure 8.

Figure 7. Two-sample t test for Striped Plate and Bubbled Plate

Figure 7 displays the results from the two-sample t Test conducted using the data

from the Striped Plate and the Bubbled Plate. These results indicate that the null hypothesis

was failed to be rejected at an alpha level of 0.05. The t-value of 1.29 produced a p-value of

0.19. This value is larger than the alpha level. There is about a 19% of results like this

occurring by chance alone if the null hypothesis is true. This means that the Striped Plate

and Bubbled Plate provided the same amount of signal interferences and allowed for similar

amounts of radio signals to penetrate.

Figure 8. Two-sample t Test for Base Plate and Concave Up Plate

Figure 8 displays the results from the two-sample t Test conducted using the data

from the Base Plate and Concave Up Plate. The t value calculated to equal 4.82. This

correlates to a p-value of essentially zero. The null hypothesis can be rejected at an alpha

level of 0.05. This means that there is almost no chance of results this extreme by chance

alone, if the null is true. This also means that the Base Plate and Concave Up Plate

structures have different signal strengths and cause different amounts of interference on the

transmission of radio waves.

Conclusion

The purpose of this experiment was to determine which of the different steel

structural designs had the greatest effect upon the signal strength of radio waves. The

different steel structures were different steel plate designs that were used to cause

interference with cell phone signals. The plates that were being tested were Solid Plate,

Bubbled Plate, Striped Plate, Concave-Up Plate, and Concave-Down Plate. These plates

were placed on top of a cell phone and allowed to interfere with the cell phone signals being

transmitted to and from the phone. An application on the cell phone displayed the signal

strength. The signal strength of any cell phone ranges from -60 dBm to -130 dBm, -60 dBm

being excellent reception with the highest possible signal strength, -130 dBm being no

reception at all with the lowest possible signal strength. To verify that the application was

working correctly, the cell phone was wrapped in aluminum foil and observed, it had a

signal strength of about -128 dBm during this. This was done to mimic a Faraday Cage,

which is an instrument used to jam radio signal. The hypothesis stating that the Concave

Down Plate would cause the most amount of signal interference, and that Concave Up Plate

would cause the least amount of interference was accepted. The highest signal strength, with

no plate was -75 dBm, with a Base Plate or control trial. The highest signal strength

attainted by a trial with a plate in play to cause interference was -77 dBm, with the

Concave Up Plate. The lowest signal strength was 106 dBm, with the Concave Down Plate.

Evidence that supports this decision includes the results from the ANOVA test and results

from the two-sample t tests. The results from the ANOVA test concluded that not all of the

structures produced the same amount of interference. Based on the results of the ANOVA

test and the two-sample t tests, the null hypothesis, that all the structures interfered the same,

was rejected. With a p-value of essentially 0 in the ANOVA test, it was concluded that there

is almost no chance of collecting this data by chance alone if all the structures blocked the

same amount of signals. However, some of the data from the structures overlapped with one

another. Consequently, there were two-sample t tests conducted in order to compare this

overlapping data. The data produced by the Bubble Plate overlapped with that of the Striped

Plate, and the data from the Base Plate overlapped with that of the Concave Up Plate. With a

p value of 0.1997, the t test concluded that the Bubble Plate and the Striped Plate produced

the same amount of interference. This is due to the fact that both of these plates allowed for

the same amount of radio waves to escape and penetrate through the plate. These two plates

also had similar surface areas. Another two-sample t test was conducted in order to compare

the data from the Base Plate to that of the Concave Up plate. The p value for this t tests was

calculated to be approximately 0, indicating that the Concave Up Plate produced more

interference than the Base Plate. A box plot of all the data is shown in Figure 5. From this

box plot it is concluded that the structures produced different amounts of interference, as

there is minimal overlap. The box plot indicates that the Concave Up Plate produced the

least amount of interference, while the Concave Down Plate produced the most amount of

interference. This supports the hypothesis.

This conclusion is supported by the research of Regina Meisels, a researcher for the

Austrian Science Organization. Meisels tested the propagation, path and behavior of an

electromagnetic wave, properties of electromagnetic waves when aimed and sent through

different rock structures such as rounded and rough edged rocks. In her findings Meisels

concluded that the rock structure played a pivotal role in the strength of the waves that

transferred through. Similarly, it was found that the design of each steel plate plays a key

role in the propagation of the cell phone signals, and consequently the cell phone signal

strength. Meisels found that rounded rock and smooth surfaced rocks produced the strongest

signal strengths (Meisels). This coincides with the data collected from the Concave Up

Plate. Likewise, the upward curve-like structure of the Concave Up Plate allowed signal

strength to prorogate from the sides and be transmitted. Most satellite dishes are also shaped

in this manor, an upward facing curved plate. However, satellite dishes produce all of the

electromagnetic radiation, in the form of radio waves, and then transmit that radiation. In

this experiment, the Galaxy S6 cell phone was producing the radiation, and only portions of

that radiation were being absorbed by the plates. The unique shape of an upward curved

satellite dish increases the signal strength of electromagnetic waves because the waves are

allowed reflect to a focal point, and then be concentrated together and faced in the direction

in which they should be transmitted. Similarly, the Concave Up Plate produced the least

amount of interference. A diagram is shown below as to why this might have happened.

Base Plate (No Plate) Concave Up Concave Down

Figure 9. Diagram of Radio Waves

Figure 9 shows the possible reasons for why these results occurred. The Base Plate

produced the highest signal strength, as it had no plate interfering with it. The Concave Up

Plate produced the highest signal strengths of all of the plates. The Concave Up Plate was

closer to the cell phone and the radio waves. This may have allowed it to absorb the waves

and transmit them to a focal point that is represented with a dot on the diagram, similar to

how a satellite dish works. Some of the waves were diffracted by the plate, and were sent

around the plate, and some of the waves were reflected back into the box. This is why the

Concave Up Plate did not produce better signal strengths than a trial using no plate. The

Concave Down Plate produced the lowest signal strength because it was the farthest from

the source of the radio waves, the cell phone. The waves had more room to be reflected off

of the steel plate. The control trials had no plates, and thus produced the least amount of

interference.

Additionally, Meisels also found that rocks that were compressed together produced

higher levels of interference (Meisels). This correlates with the Concave Down Plate within

this experiment. The Concave Down Plate, shaped similarly to a tunnel, produced the

weakest signals. This is due to the downward curving shape of this plate. The radio waves

were the most isolated with this plate, as the plate covered the entire cell phone and was

closer than any the other plates. As a result, the radio waves were practically trapped under

the plate. Some of the waves were still absorbed by the plate, but the downward facing

curve caused for the waves to be reflected back into the box, leading to weaker signal

strength.

The difference in signal penetration of the structures can be attributed to the change

in power of the outer and innermost rays. This is explained best by the research of Feodora

Berz from The Institution of Electrical Engineers. In his experiment Berz tested microwaves

to identify the effect of diffraction on the power of the wave. The power difference between

the outermost rays and the innermost rays was about 0.05% (Berz). This explains why

structures that block off the outermost rays have lower penetrating abilities, and structures

that allowed more outer rays produced a higher signal strength (i.e. the Concave Up Plate

produced the best signal strength and the Concave Down Plate produced the worst signal

strength).

As in any experiment, there were some errors. One of the errors that could have

altered the data was the fluctuations of signals by cell towers. Most of the times the signals

that were collected varied by 3 to 4 dBm. This variation was most likely caused by

atmospheric fluctuation, such as different wind patterns and moisture in the atmosphere.

Randomization of the trials was implemented as a way to counteract this and reduce any

bias present. In order to minimize this fluctuation, the experiment could be conducted in a

controlled lab environment with a transmitter and receiver. This experiment used cell phone

signals, which are radio waves, which generally operate at a frequency of 1,900 Mhz. To

further look into this field of research different frequencies can be tested. This could be done

by testing different parts of the electromagnetic spectrum, such as microwaves or infrared

waves. All of the structures in this experiment were made out of steel, different materials

such as aluminum or lead can be tested. This research is relevant because it shows which

structural designs should be used for what purpose. For example, a military bunker should

be dome shaped in order to prevent radio signals from escaping or entering. An office

building or a satellite dish should be arc shaped upward in order to minimize the amount of

signal interference.

Appendix A: Constructing Plates

Materials:

JET 15” Model Drill Press Wiss 7” Metal Shear Scissors 36” X 36” Steel Plate 1/16” Thick Twist-It Ruler1/8” Drill Bit

Procedures:

1. Use the ruler to measure out a four 7” X 7” square plates from the steel plate.

2. Use the shears to cut out these four square plates.

3. Take one of the newly created plates and bend it such that it has a curve. The plate should be curved such that the length from one side to the other is 5” and the height of the plate should be 2”. This is the Concave Up and Concave Down Plate.

4. Take another plate and cut it into four even rectangles, such that each rectangle has a width of 1.75” and a height of 7”. These are the steel plate slits that will be used for the Striped Plate.

5. Take another plate and drill nine holes evenly amongst the plate using the drill press and drill bit, be sure to clamp down the plate before drilling. This is the Bubbled Plate. The holes are drilled 0.75” away from each other and 1” away from the border of the plate.

Diagrams:

Steel Curved Plate Steel Solid Plate Steel Bubbled Plate

Metal Shears Steel Plate Slits Twist-It Ruler CalculatorFigure 10. Materials

Figure 10 shows the materials that were to create the plates, and it also shows what

the finished plates should look like. The drill press and the drill bit are not shown within this

picture.

Appendix B: Sample Calculations

One Way Analysis of Variance Test (ANOVA):

An ANOVA test compares all of the samples to one another in order to determine

whether or not the effects for each individual factor were equal to one another. This is done

by comparing the means to one another. The variables and equation used for an ANOVA

test are shown below. There is also a sample calculation provided.

X=n1 x1+...+ni x i

N

x=each sample¿¿

n=each sampe¿¿

x1=each samplemean

N=totalobservation∈all samples

MSG=n1 ( x1−x )2+...+ni ( x i−x )2

I−1

MSE=(n1−1 ) s1

2+...+(ni−1 ) s i2

N−I

n=obsevations∈eachsample

s=standard deviaion of eachsample

N=number of observation∈all samples

I=number of populations

F= MSGMSE

=Mean square groupMeansquare error

F = Variation among sample means between each population variation among individuals in all sample of each populationFigure 11. Variables and Notation for ANOVA Test

Figure 11 lists the different variables and equations that are needed in order to conduct an ANOVA test. A sample calculation is shown in the figure below.

MSG=

30 (−77.933−−88.15 )2+30 (−83.7333−−88.15 )2+30 (−104.06−−88.15 )2

+30 (−79.966−−88.15 )2+30 (−93.866−−88.15 )2+30 (−86.33−−88.15 )2

6−1

MSE=

(30−1 ) 1.652+ (30−1 ) 1.362892+ (30−1 ) 1.57422+ (30−1 ) 1.607812

+(30−1 )1.4322+(30−1 ) 0.9942362

180−6

F= 2879.912039342.1137095019826

F=1362.4918829379

Figure 12. Sample Calculation for One Way Analysis of Variance Test

Figure 12 shows how the ANOVA test was conducted. The F - value of 1362.49 was

compared to a F table in order to calculate the p – value. The data that was used in this

sample calculation is from all of the data within this experiment, shown in Table

Two-sample t -Test :

To analyze the number of standard deviations away the data lies from the sample

mean, t, a two-sample t- test was conducted. In this equation, the difference of the sample

means is taken. This is divided by the square root of the sum of both standard deviations

divided by the number of trials. The variable x1 is the mean of the first sample dBm. The

variable x2 is the mean of the second sample dBm. The variable s1 is the standard deviation

of the first sample. The variablen1 is the number of trials that were conducted for the first

sample. The variable s2 is the standard deviation of the second sample. The variablen2 is the

number of trials that were conducted for the second sample. The p - value is calculated by

comparing the t - value with the degrees of freedom on a t Table. An alpha level of 0.05 was

used. The following equation was used to calculate the t value. t=

x1−x2

√ s12

n1+

s22

n2

A sample calculation of this two-sample t test is shown in the figure below. This

calculation shows the two-sample t test for the Striped Plate and the Bubbled Plate data.

t=x1−x2

√ s12

n1+

s22

n2

t=−86.333333 dBm−−86.7333333 dBm

√ 0.9942362

30+ 1.362892

30

t=1.29869

Figure 13. Two-sample t test Sample Calculation

Figure 13 shows how the two-sample t test was conducted. The t - value of 1.29869

was compared to a t table in order to calculate the p – value. The data that was used in this

sample calculation is from the Striped Plate and the Bubbled Plate. This data is shown in

Table 1.

Appendix C: Professional Contact Conversation

Nafis Jaigirdar <nafisjaigirdar@gmail.com>

Research follow up16 messages

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Thu, Oct 8, 2015 at 7:42 AM

To: David Cinabro <cinabro@physics.wayne.edu>

Hi Mr. Cinabro I still have not heard back from you on who I can contact for my research. Currently I am on the per experimental possess and have finished the review of lit portion of my paper. If you know anyone that would be interseted in helping a great cause please send them my info thank you 

Nafisjaigirdar@gmail.com

Problem Statement: To determine how different structural designs affect the propagation of electromagnetic waves.

David Cinabro <cinabro@physics.wayne.edu> Thu, Oct 8, 2015 at 8:07 AM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Hi Nafis

        I will be happy to help.  When can we talk?  Can you come down to Wayne State and meet?  Can I come out to meet you?

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Fri, Oct 9, 2015 at 8:27 AM

To: David Cinabro <cinabro@physics.wayne.edu>

Hello,

Well, I guess we can just communicate through email for now and and if needed we can set up a time we can meet either in person or via skype (if you wanna talk about the research in depth skype would be the best way). So far we have finished the background research needed and are planning our first day of data collation today after school. If you could take a look at the document so far and let us know if there's anything we could add to the propagation of the waves it would be very helpful. So far our basic understanding is that propagation is the way a wave moves similar to diffraction. This document is essentially an explanation of the research others have completed and how it helps our understanding of the science behind our experiment. 

It would also be wonderful if you can stop by and watch our presentation in January just as a heads up.

Anyways, we will keep in touch, and thanks again for taking your time to respond to help us.

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Review of Literature & work cited.docx21K

David Cinabro <cinabro@physics.wayne.edu>Tue, Oct 13, 2015 at 7:33

AM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Hi Nafis

        I read through your literature review.  I am still not clear what you are trying to do.  The propagation of waves can be very complex.  What exactly are you trying to test and how are you doing it?

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Wed, Oct 14, 2015 at 9:07 AM

To: David Cinabro <cinabro@physics.wayne.edu>

I think these may clarify some of the misunderstandings you may have. Thank you for your help

[Quoted text hidden]

3 attachments

Problem Statement2.docx14K

Preliminary Experimental Design2.docx19K

_seniorresearchcontract_tips_1.doc26K

David Cinabro <cinabro@physics.wayne.edu> Wed, Oct 14, 2015 at 9:21 AM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Hi Nafis

        This makes things clear.  What is your "structure"?  A picture or drawing of an example would help to clarify.

        Have you thought about entering the Junior Science and Humanities Symposium?  The web site is:

http://coe.wayne.edu/ted/science/jshs-index.php

You would have to do a write up and at the Symposium in March give a talk and present a poster.

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

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Nafis Jaigirdar <nafisjaigirdar@gmail.com> Fri, Oct 16, 2015 at 8:08 AM

To: David Cinabro <cinabro@physics.wayne.edu>

Thank you this is perfect we were already making a poster for the MMSTC science fair in march however we are a group and this competition is for singles so unfortunately we cant enter. 

These are some of the structures we will be testing in the picture.

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image.jpeg236K

David Cinabro <cinabro@physics.wayne.edu>Mon, Oct 19, 2015 at 11:41

AM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Group projects have been presented before, with one person representing the group.  I have been telling them for years that they need to do something to deal with group efforts which are increasingly common in science.

        Structure?  It looks like a box.

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

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Nafis Jaigirdar <nafisjaigirdar@gmail.com> Mon, Oct 26, 2015 at 8:14 AM

To: David Cinabro <cinabro@physics.wayne.edu>

sorry i haven't been keeping you updated on our experiment however we have finished our data collection and are currently starting a statistical anova test. 

also yes these are steel plates we placed a phone in it and tested the strength of the signal that travels through

here is the final experimental design it should do a better job at explaining and it includes better visual figures. Also could you take a look at the data we collected i think its interesting how the concave down plate had the worst signal strengths i was expecting the solid to have the worst.

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3 attachments

DATA.tns5K

data.xlsx12K

Experimental Design.docx807K

David Cinabro <cinabro@physics.wayne.edu>Wed, Oct 28, 2015 at 3:07

PM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Have you tried with a different sort of phone?

        Is the box always orientated in the same way?  That is it always facing east or whatever?  Have you done a test to see if that matters?

        Does the signal strength depend on the presence of other cell phones being nearby?  I think it does not, but have you checked?

        In principal no signal should be able to penetrate a box made of conducting material, which is called a Faraday Cage.  Have you tried to build such an object?  It is very hard, but perhaps you could wrap a phone in aluminum foil and show that no signal gets through.

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Thu, Oct 29, 2015 at 8:22 AM

To: David Cinabro <cinabro@physics.wayne.edu>

yes we have tried multiple phones and they have provided similar results with a few variations based on the antenna on the phone itself.

because all the data was collected in consecutively after each other we never had to move the box so yes it was orientated in the same way. The positioning of the box does not matter as much simply because the change falls with in our range of data anyways. (it was orientated perpendicular to a cell tower)

we have not tried to build a Faraday Cage. all of our tests were ran using a steel safe box. That is a interesting concept however we were aiming to identify the build that allowed the most signals, so I'm not sure how i can us a Faraday's Cage in our experiment.

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David Cinabro <cinabro@physics.wayne.edu> Fri, Oct 30, 2015 at 1:46 PM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        The point of a Faraday cage is to see if you measure zero when you should.  It is done all the time in science to make sure you are not getting fooled by false signals.

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com>Wed, Nov 11, 2015 at 7:22

AM

To: David Cinabro <cinabro@physics.wayne.edu>

Hi sorry for the slow response I have been occupied with the data analysis and observation of our paper. I am happy to say that I have conducted test using foil as you suggested and the tests came up with no signals so the Faraday cage works. currently we are finishing up our data analysis and will start our intro and abstract next week then we start are conclusion the following week

I would also like to take this time to thank you for taking time out of your day to help us out the suggestions and questions you have added truly helped us get a better understanding of the research and further enhanced our paper.

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Mon, Nov 16, 2015 at 8:42 AM

To: David Cinabro <cinabro@physics.wayne.edu>

Hi Mr. Cinabro

I am happy to say we have finished our data analysis and are now working on the intro and conclusion we are planing to finish the final paper some time in December and i will be sure to send you a copy 

Once again i would like to take this time to thank you and invite you to our presentations with will be some time between 1/6-1/8 i will give you an exact data as the day approaches. I think you will be impressed with the amount of preparation my fellow students and i take in our research. 

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David Cinabro <cinabro@physics.wayne.edu> Tue, Nov 17, 2015 at 11:06 AM

To: Nafis Jaigirdar <nafisjaigirdar@gmail.com>

        Let me know.  I should be in town and would be interested to see.

David Cinabro, cinabro@physics.wayne.edu 313-577-2918http://motor1.physics.wayne.edu/cinabro.html

[Quoted text hidden]

Nafis Jaigirdar <nafisjaigirdar@gmail.com> Fri, Dec 11, 2015 at 9:03 AM

Draft To: David Cinabro <cinabro@physics.wayne.edu>

[Quoted text hidden]

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