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
Copyright 2019 Raiarii Jithame. Known as Arii
All Rights Reserved
BRIGHAM YOUNG UNIVERSITY - IDAHO DEPARTMENT
APPROVAL
of a senior thesis submitted by
Raiarii Jithame. Known as Arii
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
Raiarii Jithame. Known as Arii
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
3.3 Screen shot of acoustic field recorder 2 . . . . . . . . . . . . . . . . . 20
3.4 Screen shot of acoustic field recorder 3 . . . . . . . . . . . . . . . . . 20
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:
4 Chapter 1 Introduction
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.
1.5 GEM-63 Rocket Motor Engine
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
6 Chapter 1 Introduction
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]
1.5 GEM-63 Rocket Motor Engine
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
Chapter 2 Detection of Speaker Directivity Using a Lock-in Amplifier
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 2 Detection of Speaker Directivity Using a Lock-in Amplifier
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]
20 Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor
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]
22 Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor
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]
24 Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor
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.
30 Chapter 3 Sound pressure measurements of the GEM-63 Static Rocket Motor
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
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).
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);
x3=binfileload(’D:\GEM-63 data 2018-09-20\55’,’ID’,100,0); x4=binfileload(’D:\GEM-63 data 2018-09-
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
x7=binfileload(’D:\GEM-63 data 2018-09-20\80’,’ID’,2,0); x8=binfileload(’D:\GEM-63 data 2018-09-
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-’)
% title(’45 deg’)
% hold on
%subplot(2,1,2)
37
%plot(t2,x2,’b-’)
%title(’50 deg’)
%hold on
%subplot(4,1,1)
%plot(t3,x3,’r-’)
%title(’55 deg’)
%hold on
%subplot(4,1,2)
%plot(t4,x4,’k-’)
%title(’60 deg’)
%hold on
%subplot(4,1,3)
%plot(t5,x5,’k-’)
%title(’65 deg’)
%hold on
% subplot(4,1,1)
% plot(t6,x6,’g-’)
% title(’70 deg’)
% hold on
%
% subplot(4,1,2)
% plot(t7,x7,’b-’)
38 Chapter A
MATLAB code
% title(’80 deg’)
% hold on
% subplot(4,1,3)
% plot(t8,x8,’r-’)
% title(’85 deg’)
% hold on
%
% subplot(4,1,4)
% plot(t9,x9,’b-’)
% title(’90 deg’)
% hold on
% subplot(4,1,4)
% plot(t10,x10,’c-’)
% title(’100 deg’)
% hold on
%subplot(4,1,3)
%plot(t11,x11,’r-’)
%title(’110 deg’)
%hold on
%subplot(1,1,1)
%plot(t12,x12,’k-’)
39
%title(’120 deg’)
%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;
SIL45(i)=10*log10(mean (x1(start:finish).^2)/rho0/c0/1e-12); end
Nseconds2=floor(length (x2)/fs2); for i=1:Nseconds2 start=(i-
1)*fs2+1; finish=i*fs2;
SIL50(i)=10*log10(mean (x2(start:finish).^2)/rho0/c0/1e-12);
40 Chapter A
MATLAB code
end
Nseconds3=floor(length (x3)/fs3); for i=1:Nseconds3 start=(i-
1)*fs3+1; finish=i*fs3; SIL55(i)=10*log10(mean
(x3(start:finish).^2)/rho0/c0/1e-12); end
Nseconds4=floor(length (x4)/fs4); for i=1:Nseconds4 start=(i-
1)*fs4+1; finish=i*fs4;
SIL60(i)=10*log10(mean (x4(start:finish).^2)/rho0/c0/1e-12); end
Nseconds5=floor(length (x5)/fs5); for i=1:Nseconds5 start=(i-
1)*fs5+1; finish=i*fs5;
SIL65(i)=10*log10(mean (x5(start:finish).^2)/rho0/c0/1e-12); end
Nseconds6=floor(length (x6)/fs6); for i=1:Nseconds6 start=(i-
1)*fs6+1; finish=i*fs6;
SIL70(i)=10*log10(mean (x6(start:finish).^2)/rho0/c0/1e-12); end
Nseconds7=floor(length (x7)/fs7); for i=1:Nseconds7 start=(i-
1)*fs7+1; finish=i*fs7;
SIL80(i)=10*log10(mean (x7(start:finish).^2)/rho0/c0/1e-12); end
Nseconds8=floor(length (x8)/fs8); for i=1:Nseconds8 start=(i-
1)*fs8+1; finish=i*fs8;
SIL85(i)=10*log10(mean (x8(start:finish).^2)/rho0/c0/1e-12); end
41
Nseconds9=floor(length (x9)/fs9); for i=1:Nseconds9 start=(i-
1)*fs9+1; finish=i*fs9;
SIL90(i)=10*log10(mean (x9(start:finish).^2)/rho0/c0/1e-12); end
Nseconds10=floor(length (x10)/fs10); for i=1:Nseconds10 start=(i-
1)*fs10+1; finish=i*fs10;
SIL100(i)=10*log10(mean (x10(start:finish).^2)/rho0/c0/1e-12); end
Nseconds11=floor(length (x11)/fs11); for i=1:Nseconds11
start=(i-1)*fs11+1; finish=i*fs11;
SIL110(i)=10*log10(mean (x11(start:finish).^2)/rho0/c0/1e-12); end
% 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-’)
42 Chapter A
MATLAB code
%plot(SIL60,’b-’)
%plot(SIL65,’k-’)
%plot(SIL70,’r-’)
% plot(SIL80,’g-’)
%plot(SIL85,’b-’)
%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
SIL50t= SIL50(t50-5:t50+115); plot(SIL50t)
SIL55t= SIL55(t55-5:t55+115); plot(SIL55t)
SIL60t= SIL60(t60-5:t60+115); plot(SIL60t)
SIL65t= SIL65(t65-5:t65+115); plot(SIL65t)
SIL70t= SIL70(t70-5:t70+115); plot(SIL70t)
SIL80t= SIL80(t80-5:t80+115); plot(SIL80t)
SIL85t= SIL85(t85-5:t85+115); plot(SIL85t)
SIL90t= SIL90(t90-5:t90+115); plot(SIL90t)
SIL100t= SIL100(t100-5:t100+115); plot(SIL100t)
SIL110t= SIL110(t110-5:t110+115); plot(SIL110t)
title(’Sound Intensity Levels of the GEM-63 Rocket’)
legend(’SIL40t’,’SIL45t’,’SIL50t’,’SIL55t’,’SIL60t’,’SIL65t’,’SIL70’,’SIL80t’,’SIL xlabel(’Time’)
ylabel(’Decibels’)
44 Chapter A
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’)