acoustic directivity measurements of a gem-63 rocket …

ACOUSTIC DIRECTIVITY MEASUREMENTS OF A GEM-63 ROCKET

MOTOR AND OF A YAMAHA HS8 STUDIO MONITOR

by

Raiarii Jithame. Known as Arii

A senior thesis submitted to the faculty of

Brigham Young University - Idaho

in partial fulfillment of the requirements for the degree of

Bachelor of Science

Department of Physics

Brigham Young University - Idaho

December 2019

BRIGHAM YOUNG UNIVERSITY - IDAHO DEPARTMENT

APPROVAL

of a senior thesis submitted by


This thesis has been reviewed by the research committee, senior thesis coordinator, and department chair and has been found to be satisfactory.

Date Jon Paul Johnson, Advisor

Date David Oliphant, Senior Thesis Coordinator

Date Stephen McNeil, Committee Member

Date Todd Lines, Chair

ABSTRACT

ACOUSTIC DIRECTIVITY MEASUREMENTS OF A GEM-63 ROCKET

MOTOR AND OF A YAMAHA HS8 STUDIO MONITOR


Department of Physics

Bachelor of Science

One important characteristic of sound sources is the directivity, which is how

the power is radiated in different spatial directions. In this paper, two sound

sources are characterized and discussed: The GEM-63 solid rocket motor and

a Yamaha HS8 studio monitor speaker. The rocket sound was measured

approximately 1.5 kilometers away, while the speaker was characterized in a

noisy environment by using a lock-in amplifier to filter extraneous sound. The

time dependent directivity plots of the GEM-63 motor represent the first

presentation of data of this kind.

ACKNOWLEDGMENTS

As the first member in my family to get a college degree I am humbled to

be graduating from Brigham Young University- Idaho. One of the reasons I

decided to study Physics is due to the fact that I still have the imagination of a

little boy. I want to travel space and time, and fight aliens. Physics is the perfect

major for creative thinking where your imaginations can transform into

reality; physics pushes the boundaries of our wildest dreams. This experience

shaped the way I portray the world we live in and rejuvenated a greater

appreciation of God’s master plan to bring joy and peace to all of His

creatures.

Special acknowledgment to my adviser brother Johnson for the many

hours of coding and mentoring me on the applied side of science, and being a

great

teacher of life.

To the entire Faculty at Brigham Young University- Idaho Physics

Department for their help and support throughout the many months of my

under-grad

study.

Special thanks to Dr Kent Gee (who will probably never read this) for

letting BYU-I tag along the BYU acoustic team and involving us in this

marvelous journey. An acknowledgment to Adam Worden for being an

emotional support during this physics undergraduate study.

Most importantly I wanted to thank my parents for supporting me all my

life and throughout my studies and hopefully I can return the favor soon. x

Merci Papa et Maman.

This paper is dedicated to Heimana my baby boy who hopefully will

become a physicist one day. Love you.

Physics rules!

Contents

Table of Contents xi

List of Figures xiii

1 Introduction 1

1.1 The Purpose of These Projects . . . . . . . . . . . . . . . . . . . . . 1

1.2 Directivity of Sound Sources . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Lock-in Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Rocket Motor Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 GEM-63 Rocket Motor Engine . . . . . . . . . . . . . . . . . . . . . . 5

2 Detection of Speaker Directivity Using a Lock-in Amplifier 9

2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .14

3 Sound pressure measurements of the GEM-63 Static Rocket Motor 17

3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Acoustic field recorder software . . . . . . . . . . . . . . . . . 19

3.1.2 Set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.3 Materials used . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Normalized Sound Intensities at Different Angles ’Regular Plots’ . . . 25

3.3 Time Dependent Directivity Plots . . . . . . . . . . . . . . . . . . . . 26

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

Bibliography 31

A MATLAB code 33

xi

List of Figures

1.1 lock-in schematic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Photo of the GEM-63 begin firing . . . . . . . . . . . . . . . . . . . . 6

1.3 Northrop Grumman GEM-63 specifications . . . . . . . . . . . . . . . 7

2.1 HS8 project directivity schematics . . . . . . . . . . . . . . . . . . . . 11

2.2 Polar plots of the HS8 speaker at different octaves . . . . . . . . . . . 13

2.3 Comparing our data to YAMAHA . . . . . . . . . . . . . . . . . . . . 15

3.1 Google Earth bird eye view of the launch . . . . . . . . . . . . . . . . 18

3.2 Screen shot of acoustic field recorder 1 . . . . . . . . . . . . . . . . . 19



3.5 Personal picture 85◦ facing the rocket . . . . . . . . . . . . . . . . . . 21

3.6 Personal picture 85◦ side view . . . . . . . . . . . . . . . . . . . . . . 22

3.7 Personal picture 85◦ microphones set up . . . . . . . . . . . . . . . . 23

3.8 Personal picture 85◦ equipment . . . . . . . . . . . . . . . . . . . . . 24

3.9 Personal picture 85◦ closer look at equipment . . . . . . . . . . . . . 24

3.10 Sheet material specifications . . . . . . . . . . . . . . . . . . . . . . . 25

3.11 Sound pressure levels plot from each stations . . . . . . . . . . . . . . 26

3.12 Top to bottom plot SPL . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.13 Predicted OASPL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

xiii

Chapter 1

Introduction

1.1 The Purpose of These Projects

The purpose of these projects is to study and analyze sounds to determine the sound

pressure level and directivity of the source. The first project I participated was with

Dr Jon Paul Johnson at Brigham Young University-Idaho (BYU-I) in the spring

semester 2018 was to detect the directivity of a speaker. To detect the directivity of

the speaker we used the lock-in amplifier which I will explain in its respective section.

The second project was accomplished with the collaboration of Brigham Young

University (BYU) acoustic team led by Dr Gee, an expert in that field, during the

summer of 2018. We focused our study on the GEM-63 rocket motor engine. Using

both 6.35 mm and 12.7 mm microphones and have a sampling rate at around 50000

Hz stationed and positioned at different angles from the sound source, we collected

data which will help us better understand how loud this new and improved rocket

engine is and we could also determine other characteristics such as; the energy or

position of the object firing. Part of this paper will cover the methods and calculations

we used to analyze the sound intensity levels and directivity plot of the rocket motor

engine.

1

2 Chapter 1 Introduction

1.2Directivity of Sound Sources

One of the most important characteristics of sound sources is how the sound power

is radiated in different directions. We hear sound or noise every day, but we do not

think of the physics behind it. For examples, our own voice or the movies we watch,

the music we hear-what is the physics behind it? How does it work? I think

understanding these characteristics of sound is very interesting and could help other

people who can’t hear sounds. One example I would like to take a moment to describe

is the characteristics of the sound of people’s voice. We know that when sound is

produced air molecules moves in space, and the movements of these molecules forms

waves. The shape of the wave will determine the identity of the sound (high, low, etc.).

Depending where you stand you will hear the sound differently, thus the sound you

hear will dependent on your location from the sound source (distance, altitude, angle,

etc.). Therefore, when we have to communicate to another person from a great

distance, we cup our hands and shout things and that is to alter the directivity, thus

there will be a greater chance that the other person might hear you. Similarly, the

same thing happens with musical instruments, but this is a little more complicated,

because musical instruments can have many complex shapes, which results in

different sounds. The study of directivity of sound sources is important and has many

benefits and applications from it, such as locating sound sources, which the military

uses, echo location, the study of sound intensity of machines, and noise control. All of

these could help our community be more livable.

1.3Lock-in Amplifier

One of the major components we used in detecting the direction of the sound source

is by using the lock-in amplifier (LIA). Because we lack an anechoic chamber this

3

1.3 Lock-in Amplifier

tool is to help us filter unwanted sound for clear detection of sine waves output to the

speaker. A LIA is what we used to detect and measure a very small AC signal from our

microphone in the presence of room noise. The LIA can provide accurate

measurement even when small signals are obscured by noise sources many

thousands of times larger [6]. LIAs are sensitive to a component of the signal at a

specific reference frequency and phase. Noise signals, at frequencies and/or phases

other than the reference frequency, are rejected on integrating the signal. Our speaker

was excited at various fixed reference frequencies and the LIA detected the response

from the microphone at the same reference frequencies. We used a sinusoidal wave

generator in LabVIEW to produce our reference signal. ” What exactly does the lock-

in measure? Fourier’s theorem basically, states that any input signal can be

represented as the sum of many sine waves of differing amplitudes, frequencies and

phases. This is generally considered as representing the signal in the” frequency

domain”. Normal oscilloscopes display the signal in the” time domain”. Except in the

case of clean sine waves, the time domain representation does not convey very much

information about the various frequencies which make up the signal. In the general

case, the input consists of signal plus noise. Noise is represented as varying signals at

all frequencies. The ideal lock-in only responds to signal at the reference frequency.

Noise at other frequencies is removed by the notch filter following the multiplier.

This” bandwidth narrowing” is the primary advantage that a lock-in amplifier

provides. Only inputs with frequencies at the reference frequency result in an output”

[6] Let’s look at an example. Suppose the input signal is a simple square wave at

frequency f. The square wave is composed of many superposed sine waves at

multiples of f with related amplitudes and phases. A 2 V peak to peak (Vpp) square

wave can be expressed as:


Figure 1.1 In the diagram, the external reference, the lock-in’s reference, and

the signal are all shown. The lock-in amplifies the signal and then multiplies

it by the lock-in reference using a phase-sensitive detector or multiplier [4]

S(t) = 1.273sin(ωt) + 0.4244sin(3ωt) + 0.2546sin (5ωt + ...) + ... (1.1)

1.4Rocket Motor Acoustics

This paper discusses the measurements set ups, correlation analyses are used to

understand the frequency and characteristics of the noise as a function of angle.

One of the most rewarding parts of being a physics major is to see results from

hard work taking place right in front us-even when it is not your work - and

experiencing the works of other brilliant scientists and engineers are in my opinion

more beautiful that seeing all the artwork residing within the Louvre museum. The

horizontal test launch of the GEM-63 rocket strapped booster motor engine did not

disappoint. As technology continues to improve, our curiosity will also continue to

increase, and as we push the boundaries of discovery, we want to go smaller, deeper,

and farther into the unknown. This area of study is new to me; however, BYU acoustics

has

5

1.5 GEM-63 Rocket Motor Engine

been studying the acoustics of rocket engines for a while and they also study fighter

jet engines noise in depth. ” The development of the next-generation space flight

vehicles has prompted renewed interest regarding source characterization and

nearfield propagation models of rocket noise. This source characterization is

required to determine the vibroacoustic [8] impact on flight hardware and structures

in the vicinity of the launch pad. Measurements of the noise near the rocket plume is

critical, not only to directly determine the noise environment, but also to provide

inputs to empirical models and to validate computational aeroacoustics models” [8]

My understanding of the purpose of this project is to study how loud these new rocket

motors are in order to determine the limits at which it is safe for the human hearing

to live in a comfortable setting. According to Dr Gee, in the near future there will be

dozens new rocket launch sites around the country, thus it is imperative that we get

these data.


The Northrop Grumman test launch site is conveniently located in the northern part

of Utah-an ideal location for BYU-I physics students to personally experience the

sheer power of those rocket motor engines. ”In 2018, Northrop Grumman reported

they will conduct a full-scale static fire test of the GEM-63, the company’s next

generation of Graphite Epoxy Motor (GEM) family (figure 1.3) of strap-on boosters to

support intermediate- and large-class space launch vehicles, in Promontory, Utah.

This motor was developed in partnership with United Launch Alliance to support

national security, science and commercial payload launches of its Atlas V vehicle

starting in 2020. At 66 feet long, the 63-inch diameter motor will fire for


approximately 100 seconds and produce approximately 359,000 pounds of thrust.

The next

Figure 1.2 GEM-63 firing at 1:00 PM 09/20/2018, as seen from one site where sound measurements were made [1]

steps in Northrop Grumman’s propulsion system development include testing,

casting and static firing the new solid rocket motors. Full scale qualification testing is

planned to begin this year.” [5]


7

Figure 1.3 Specifications of the GEM rocket motors family. [5]

8

Chapter 1 Introduction

Chapter 2

Detection of Speaker Directivity

Using a Lock-in Amplifier

2.1 Methods

Last summer I was doing some research here at BYU-I to study the directivty of the Yamaha

HS8 with Dr Johnson before the GEM-63 research opportunity came. We developed LabVIEW

code, which will be included in this code appendix. Dr Johnson and Joseph Harris a, BYU-I

physics undergrad student, continued working on this project and collected the data in the

upstairs lab for the Yamaha HS8 directivity using a lock-in amplifier.

The schematic below in figure 2.1 shows the set up with the instruments used for this

project. Because we do not have an an-echoic room we needed to find a way to reduce noise.

To minimize reflection, we used a sound absorbing chamber. The way we improved the

signal-to noise ratio is by using the Lock-in Amplifier (LIA). The signal from the speaker,

picked up by the microphone, has the noise filtered out by the LIA, which we wanted to check

against measuring in an an-echoic chamber. The

9

speaker was mounted on a turntable tripod and inserted in a noise absorber chamber found

in the upstairs laboratory. In the schematic the speaker is connected to the NI cDAQ-9174

Chassis and LabVIEW VI. The LabVIEW enables the frequencies to change over time and

produce a frequency sweep at every 1/3 octave. The analog out 1 from the NI cDAQ-9174 is

wired to the reference channel of the LIA which generate the reference frequency matching

10 Chapter 2 Detection of Speaker Directivity Using a Lock-in Amplifier

the

speaker. The microphone we used was a PCB 378B02 condenser 1/2-inch diameter

microphone facing directly at the speaker and is connected to signal conditioner PCB 480C02

for the main purpose of powering it. Between the signal conditioner and the LIA, we had a

oscilloscope wired up and it does not show up in the schematic, but it is there. The signal

conditioner output is linked to the LIA In channel. The R channel from the LIA is linked to the

DAQ, which is connected to the LabVIEW. It is importance to note the R channel from the LIA

is not phase dependent on the reference signal. Finally, when everything is set up, we can

start taking data, and the speaker turntable needs to be manually pivoted

360 degrees in the absorbing chamber.

11

2.2 Results

Figure 2.1 Schematic of the set up we had in the up stairs lab [2]

2.2 Results

From the directivity polar plots of the speaker obtained in figure 2.2 we can see data were

successfully collected with results to analyze. As predicted the polar plots from the lower

frequency range (25-400 Hz) were somewhat uniform. As we continued increasing the

frequency can wee the directivity polar plots getting distorted and that is due to the

12

Chapter 2 Detection of Speaker Directivity Using a Lock-in Amplifier

destructive interference from the room and speaker. Upon analyzing the results from the

polar plots obtained we see something that does fit the model and if you take a closer look at

the 100 Hz you can see that the frequency at 180 degree is slightly larger than the 0 degree

and that should not be happening, and we do not know why. However, we assume it is caused

by the reflection of the sound from the back panel of the absorbing chamber or it could be

because the speaker is ported.

Further experiments are required to have a better understanding.

13

2.2 Results

14


Figure 2.2 All polar plots with schematic showing how the angle is measured. Results of different octaves are shown. [2]

2.3 Conclusion

The difficulty of this project was to take acoustical measurements without an-echoic

chamber. From the results in figure 2.2 tells us that it is possible to have good data even

without an an-echoic chamber and that is due with the help of the lock-in amplifier. In figure

2.3 are two graphs representing the SLP on the vertical axis and frequency on the horizontal

axis. The top is our results and the bottom is what YAMAHA came up in their lab. The results

are stunning and proves that measuring the directivity of a sound source in a noisy room is

possible. Future work for this experiment is to take measurements in a less noisy room or

conduct the project outside where sound cannot reflect as much. An alternative solution is

to go the BYU and use their anechoic chamber, where they have all the fancy stuffs.

15

2.3 Conclusion

Figure 2.3 Comparing our SPL vs frequency from 10 Hz-20,000 Hz vs Yamaha 10 Hz-50,000 Hz. We did not go to 50,000Hz this is why we don’t see the fall out in our graph. [2]

16


Chapter 3

Sound pressure measurements of the

GEM-63 Static Rocket Motor

3.1 Methods

Far-field acoustical measurements were made on two separate occasions for the GEM63

motor. September 20th, 2018 was the first test launch day for the GEM-63 rocket motor

engine. BYU acoustics team has kindly invited us to join their research group and offered us

three stations to set up and measure. Our stations were (85, 90, 100 degrees). There were

four students from BYU-I who drove down to the test launch location early in that morning

accompanied by Dr Johnson. At 85 degree me and Will, another BYU-I physics student set up

our station. Specific materials for set up is in the appendix: Rocket materials set up. At 90,

degree Noah from BYU-I set up his station. At 100-degree Lydia Harris set up her station.

Additionally, BYU Acoustics set up ten other stations, at 40, 45, 50, 55, 60, 65, 70, 80, 110,

and 120 degrees (figure 3.1). All data were collected and have been included in the appendix:

MATLAB.

17

18 Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor

Figure 3.1 Test site launch in Promontory, Utah. Microphones stationed from 40 ◦ to 120 ◦ ,

at the source is the ATK test site where the GEM-63 engine is located. BYU-I were located at

85, 90, 100 ◦. [1]

3.1 Methods 19

3.1.1 Acoustic field recorder software

One of the biggest issues we had on the test site was to figure out how to use the

acoustic software (Acoustic field recorder). I will include pictures (figures: 3.2, 3.3,

3.4) and description in the caption on how to use the software for future students

willing to use it in the future.

Figure 3.2 How to use the AFR step 1 [2]


Figure 3.3 How to use the AFR step 2 [2]

Figure 3.4 How to use the AFR step 3. There nothing showing in the picture, because nothing was plugged in during the screenshot. As you connect everything you will see things moving and ready for calibration and experiment. [2]

3.1 Methods 21

3.1.2 Set up

In the figures: 3.5, 3.6, 3.7, 3.8, 3.9 are the station set ups and descriptions are the

figure caption.

Figure 3.5 Set up of our 85 ◦ station looking directly at the source. Will (a student from BYU-I is sitting in the chair calibrating our microphones).Notice three tripods in our set up (microphones, weather station and a gopro.). [1]


Figure 3.6 Closer look at our set up and microphones and computers from a side view. Notice in the background is BYU team. [1]

3.1 Methods 23

Figure 3.7 3 microphones probes secured on the arm stand using strong and handy black tape found in the back of the car are oriented directly at the source. Notice in the back is BYU-I 90◦ station. [1]


Figure 3.8 Microphones were calibrated and connected to the DAQ system and linked to the BYU-I acoustics laptop. [1]

Figure 3.9 A closer look at our station, DAQ system in view and hooked up on our laptop. [1]

25

3.2 Normalized Sound Intensities at Different Angles ’Regular Plots’

3.1.3 Materials used

Figure 3.10 The chart of materials used for the GEM-63 measurements [1]

3.2 Normalized Sound Intensities at Different Angles

’Regular Plots’

Using MATLAB we have plotted the sound intensity levels of the rocket motor at each angle

using the sound pressure level equation. SPL = 20 ∗ Log10(p/pf) where SPL is the Sound

pressure and level pf = 2 ∗ 10−5 Pa is the reference sound pressure. (Figure 3.11)

The result is a normalized sound pressure levels at each angle. We see stations

65, 60, 55 were the loudest at about 120 dB. The lowest SPL were the ones far off at 110, 120.

Stations 110 and 120 were located behind a hill that explains the data on the graph.

26

Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor

Figure 3.11 Normalized sound pressure levels at each angle [1] [2]

3.3 Time Dependent Directivity Plots

After we have calculated and plotted the sound intensity levels at each station, we came up

with a plot of time vs angles. According to Dr Gee this graph is one of a kind and no one has

attempted to create this plot. [3]

From figure 3.12 we can different colored zone telling us the pressure levels at different

angles at different times. The red zone is where the sound is mostly located, the darker zone

27

is where the loudest points are as previously seen in figure 3.11. We can see a distinct area

where the loudest points are from 55-70 degrees. It seemed odd

3.3 Time Dependent Directivity Plots

at first that the concentration was located at that spot. I was expecting 40, 50 degrees to be

the loudest, because there are the closest angles relative to the rocket plume.

Figure 3.13 is an angle vs OASPL (dB) by (M M. James, A R. Salton. K L. Gee,T B. Neilsen, S

A.McInerny, R J. Kenny) who came up with this model supporting what we got in our results.

The red zone is shown at about 50-60 degrees relative to the rocket plume. The area of

highest intensity is indeed located at 50-60 degrees relative to the rocket plume. This

phenomenon is due to the turbulence in the plume and shock wave of the intense outgoing

jet stream.

28

Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor

Figure 3.12 Time vs angles SPL. The horizontal axis is representing the angle and the vertical axis is time, with the SPL represented by the color. Color bar unit in decibels. [1]

[2]

Figure 3.13 https://www.semanticscholar.org/paper/Modification-ofdirectivity. Our data matches M M. James, A R. Salton. K L. Gee,T B. Neilsen, S A.McInerny, R J. Kenny.

3.4 Conclusion

Overall the measurements of the GEM-63 were good and we have results that works, and we

were satisfied. The purpose of the project was to get some acoustical data for near future

completions of new launch test site possibly located close to cities. We have some numbers

of where the sound is concentrated (The red zone, darker red zone) and the calmer ones

(Blue, and yellow). If construction companies really need to construct infrastructure near

the site, then they have an idea of the ’safe’ and ’unsafe’ zones.

29

Our data matches those of M M. James, A R. Salton. K L. Gee,T B. Neilsen, S A.McInerny, R

J. Kenny (figure 3.13) experts in that field. For future work BYU will be working with GPS

synchronization to have a better timing on the measurements.

3.4

Conclusion 29

Stations 110, 120 will have some new methods implemented for better data.

Bibliography

[1] My own sources (videos, pictures)

[2] Brother Johnson Personal Communication

[3] Dr Gee Personal Communication

[4] Simplify schematic of the lock-in amplifier www.instructables.com/

[5] Northrop Grumman 2019, ”Official website, www.northropgrumman.com (@ 2019

Northrop Grumman)

[6] About the Lock-In Amplifier, Lock-in amplifier www.thinksrs.com/downloads/

pdfs/applicationnotes/AboutLIAs.pdf

[7] Joseph S. Lawrence†, Eric B. Whiting†, Kent L. Gee, Reese D. Rasband‡, Tracianne B.

Neilsen, and Scott D. Sommerfeldt, “Three-microphine probe bias errors for acoustic

intensity and specific acoustic impedance”, J. Acoust. Soc. Am. 143 (2), EL81-EL86

(2018).

[8] Kent L. Gee, Eric B. Whiting†, Tracianne B. Neilsen, Michael M. James, and Alexandria

R. Salton, “Development of Near-field Intensity Measurement Capability for Static Rocket

Firing”, Trans. Jpn. Soc. Aeronautic. Space Sci. 14 (ists30), Po-2-9-Po-2-15 (2016)

31

http://www.instructables.com/

http://www.northropgrumman.com/

http://www.thinksrs.com/downloads/pdfs/applicationnotes/AboutLIAs.pdf



33

BIBLIOGRAPHY

[9] Kent L. Gee, Paul B. Russavage‡, Tracianne B. Neilsen, S. Hales Swift†, and Aaron B. Vaughn,

“Subjective rating of the jet noise crackle precept”, J. Acoust.

Soc. Am. 144 (1), EL40-EL45 (2018).

[10] J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, 1998), p. 23.

[11] J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses dispersive

media,” Phys. Rev. Lett. 84, 2370–2373 (2000).

[12] K. David, “Intel’s EUV lithography process line,” http://www.intel.com/

technology/silicon/lithography.htm (Accessed April 15, 2006).

http://www.intel.com/technology/silicon/lithography.htm



34 Chapter A MATLAB code

Appendix A MATLAB code

% GEM-63 SIL ARII%% clear;

close all;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%

%pf= 2.0*10^-5; % smallest sound we can hear %SPL= 20*log10(p/pf);

% Sound pressure level equation

x0=binfileload(’D:\GEM-63 data 2018-09-20\40’,’ID’,1,2); x1=binfileload(’D:\GEM-63 data 2018-09-

20\45\Data’,’ID’,2,1); x2=binfileload(’D:\GEM-63 data 2018-09-20\50’,’ID’,100,0);


20\60’,’ID’,100,0); x5=binfileload(’D:\GEM-63 data 2018-09-20\65’,’ID’,2,0); x6=binfileload(’D:\GEM-

63 data 2018-09-20\70’,’ID’,101,0);% log in wrong %time

33


20\85’,’ID’,7,0); % byui (me & will) x9=binfileload(’D:\GEM-63 data 2018-09-20\90’,’ID’,101,0);

%byui(noah) x10=binfileload(’D:\GEM-63 data 2018-09-20\100’,’ID’,12,0); %byui (lydia)

x11=binfileload(’D:\GEM-63 data 2018-09-20\110’,’ID’,100,0);

%x12=binfileload(’D:\GEM-63 data 2018-09-20\120’,’ID’,1,0);

% frequencies at each station from file fs0=51200;

fs1=204800; fs2=51200; fs3=102400; fs4=51200;

fs5=102400; fs6=51200; fs7=50000; fs8=51200;

fs9=51200; fs10=50000; fs11=51200; %fs12=51200;

tstep0=1/fs0; tstep1=1/fs1;

tstep2=1/fs2; tstep3=1/fs3;

36 Chapter A

MATLAB code

tstep4=1/fs4; tstep5=1/fs5; tstep6=1/fs6; tstep7=1/fs7;

tstep8=1/fs8; tstep9=1/fs9; tstep10=1/fs10;

tstep11=1/fs11; %tstep12=1/fs12;

t0=0:tstep0:(length(x0)-1)*tstep0; t1=0:tstep1:(length(x1)-1)*tstep1; t2=0:tstep2:(length(x2)-

1)*tstep2; t3=0:tstep3:(length(x3)-1)*tstep3; t4=0:tstep4:(length(x4)-1)*tstep4;

t5=0:tstep5:(length(x5)-1)*tstep5; t6=0:tstep6:(length(x6)-1)*tstep6;% & no data for this angle

t7=0:tstep7:(length(x7)-1)*tstep7; t8=0:tstep8:(length(x8)-1)*tstep8; t9=0:tstep9:(length(x9)-

1)*tstep9; t10=0:tstep10:(length(x10)-1)*tstep10; t11=0:tstep11:(length(x11)-1)*tstep11;

%t12=0:tstep12:(length(x12)-1)*tstep12;

% Ploting raw data

% start the subplot (an array of plots)

% subplot(2,1,1)

% plot(t0,x0,’k-’)

% title(’40 deg’)

% hold on

% subplot(2,1,2)

% plot(t1,x1,’g-’)


% hold on

%subplot(2,1,2)

37

%plot(t2,x2,’b-’)

%title(’50 deg’)

%hold on

%subplot(4,1,1)

%plot(t3,x3,’r-’)


%hold on

%subplot(4,1,2)

%plot(t4,x4,’k-’)


%hold on

%subplot(4,1,3)

%plot(t5,x5,’k-’)


%hold on

% subplot(4,1,1)

% plot(t6,x6,’g-’)


% hold on

%

% subplot(4,1,2)

% plot(t7,x7,’b-’)

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MATLAB code


% hold on

% subplot(4,1,3)

% plot(t8,x8,’r-’)


% hold on

%

% subplot(4,1,4)

% plot(t9,x9,’b-’)


% hold on

% subplot(4,1,4)

% plot(t10,x10,’c-’)


% hold on

%subplot(4,1,3)

%plot(t11,x11,’r-’)


%hold on

%subplot(1,1,1)

%plot(t12,x12,’k-’)

39


%hold on

% xnorm=x (1.5e7:length(x))/300;

% player=audioplayer(xnorm,fs);

% play(player)

% Calculate SIL for the pressure data

%SIL = 10*dB*log10(<p^2>/rho/c0/Iref) where Iref = 1x10^-12 W/m^2

rho0=1.21; % density of the air c0=343; % speed of sound

Nseconds1=floor(length (x0)/fs0);

for i=1:Nseconds1 start=(i-1)*fs0+1; finish=i*fs0;

SIL40(i)=10*log10(mean (x0(start:finish).^2)/rho0/c0/1e-12); end

Nseconds1=floor(length (x1)/fs1); for i=1:Nseconds1 start=(i-

1)*fs1+1; finish=i*fs1;




SIL50(i)=10*log10(mean (x2(start:finish).^2)/rho0/c0/1e-12);

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end


1)*fs3+1; finish=i*fs3; SIL55(i)=10*log10(mean

(x3(start:finish).^2)/rho0/c0/1e-12); end
















41







Nseconds11=floor(length (x11)/fs11); for i=1:Nseconds11

start=(i-1)*fs11+1; finish=i*fs11;


% Nseconds12=floor(length (x12)/fs12);

% for i=1:Nseconds12

% start=(i-1)*fs12+1;

% finish=i*fs12;

% SIL120(i)=10*log10(mean (x12(start:finish).^2)/rho0/c0/1e-12);

% end

%Plot SIL(t) on the bottom subplot figure

% subplot(1,1,1)

% plot(SIL40,’k-’)

% hold on

%plot(SIL45,’g-’)

%plot(SIL50,’b-’)

%plot(SIL55,’r-’)

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MATLAB code


%plot(SIL65,’k-’)

%plot(SIL70,’r-’)

% plot(SIL80,’g-’)


%plot(SIL90,’c-’) %plot(SIL100,’r-’)

% plot(SIL110,’b-’)

% plot(SIL120,’b-’)

% title(’SIL from 40 deg to 120 deg’) %

legend(’85’,’90’,’100’,’110’)

t40=24; t45=61;

t50=62; t55=64;

t60=62; t65=177;

t70=59; t80=427;

t85=40; t90=14;

t100=65; t110=55;

figure %Plotting SIL without the unwanted section of data (the ’t’ stands for SIL40t= SIL40(t40-

5:t40+115); plot(SIL40t)

hold on

SIL45t= SIL45(t45-5:t45+115); plot(SIL45t)

43











title(’Sound Intensity Levels of the GEM-63 Rocket’)

legend(’SIL40t’,’SIL45t’,’SIL50t’,’SIL55t’,’SIL60t’,’SIL65t’,’SIL70’,’SIL80t’,’SIL xlabel(’Time’)

ylabel(’Decibels’)

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MATLAB code

% contructing our gris and ploting surface plot

SILangle= [SIL40t;SIL45t;SIL50t;SIL55t;SIL60t;SIL65t;SIL70t;SIL80t;SIL85t;SIL90t;S tgrid=(1:121);

thetagrid= [40,45,50,55,60,65,70,80,85,90,100,110];

[T,Theta]=ndgrid(thetagrid,tgrid);

figure surf(T,Theta,SILangle,’edgecolor’,’none’)

title(’Surface plot time vs angles’) xlabel(’\theta’) ylabel(’t’)

zlabel(’SILangle’)

acoustic directivity measurements of a gem-63 rocket …

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