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International Baccalaureate Extended Essay
Standing Wave Thermoacoustic Refrigeration
How does the acoustic intensity affect the amount of heat moved in a standing wave
thermoacoustic refrigeration system?
Subject: Physics
May 2018
Word Count: 3995
i
Table of Contents
Table of Contents ............................................................................................................................. i List of Illustrations ......................................................................................................................... iii List of Tables .................................................................................................................................. v Introduction ..................................................................................................................................... 1 Investigation .................................................................................................................................... 2
Background ................................................................................................................................. 2 Thermoacoustics Effect........................................................................................................... 2 Standing Wave Thermoacoustic Refrigerators ....................................................................... 2
Concepts...................................................................................................................................... 4 Standing Longitudinal Wave .................................................................................................. 4 Sound Intensity ....................................................................................................................... 4 Thermal Penetration Depth ..................................................................................................... 4 Isothermal Process .................................................................................................................. 4 Adiabatic Process .................................................................................................................... 5 Polytropic Process ................................................................................................................... 5 Isobaric Process....................................................................................................................... 5 Temperature Gradient ............................................................................................................. 5 Work-Energy Principle ........................................................................................................... 6 Ideal Gas ................................................................................................................................. 6
Hypothesis .................................................................................................................................. 7 Theory ......................................................................................................................................... 7
Assumptions ............................................................................................................................ 7 The Pressure-Velocity Distribution of Particles in a Standing Longitudinal Wave ............... 7 Temperature Difference due to Thermoacoustic Effect .......................................................... 8 The Effect of Amplitude Changes ........................................................................................ 14 The Effect of Frequency Changes ......................................................................................... 16
Experiment .................................................................................................................................... 17 Objective ................................................................................................................................... 17 Brief Description of Experiment Design .................................................................................. 18 Standing wave pattern ............................................................................................................... 19 Stack Design ............................................................................................................................. 20
Thermal Penetration Depth ................................................................................................... 20 Blockage Ratio ...................................................................................................................... 21 Geometry of the Stack........................................................................................................... 22 Stack Placement .................................................................................................................... 22
Experiments Conducted ............................................................................................................ 23 Analysis of Data ............................................................................................................................ 24
Error Sources ............................................................................................................................ 24 Inaccuracy caused by Instruments and Methods................................................................... 24 Heating Effect of the Loudspeaker ....................................................................................... 24
Evaluation of Experiments........................................................................................................ 26 Thermoacoustic Effect (Experiment 1) ................................................................................. 26
ii
Effect of Amplitude change (Experiment 2) ......................................................................... 27 Effect of Frequency change (Experiment 3) ......................................................................... 28
Conclusion .................................................................................................................................... 30 Evaluation ................................................................................................................................. 30 Areas of Improvements ............................................................................................................. 30
References ..................................................................................................................................... 31 Appendix A - Materials and Tools................................................................................................ 34
Full List of Materials Used ....................................................................................................... 34 Full List of Tools Used ............................................................................................................. 35
Appendix B - Engineering Procedure ........................................................................................... 36 Stack Building........................................................................................................................... 36 Thermoacoustic System ............................................................................................................ 37 Configuration System ............................................................................................................... 39 Testing Environment................................................................................................................. 42
Appendix C - Operation Procedure............................................................................................... 45 Appendix D - Experiment Setting Data ........................................................................................ 46
Loudspeaker Data ..................................................................................................................... 46 Environment Data ..................................................................................................................... 46
Appendix E - Experiment Raw Data ............................................................................................ 47 Stack Setting 1 Data .................................................................................................................. 47 Stack Setting 2 with High Amplitude Data .............................................................................. 47 Stack Setting 2 with Medium Amplitude Data ......................................................................... 49 Stack Setting 2 with Low Amplitude Data ............................................................................... 51 Stack Setting 2 with High Amplitude and 2nd Harmonic Data ................................................ 53 Heating Effect of Loud Speaker Data ....................................................................................... 54
iii
List of Illustrations
Figure 1. Schematic illustration of the standing wave thermoacoustic refrigerator with an
acoustic driver. (Kajurek et al. 2017) ...................................................................................... 2 Figure 2. (Left) Ben & Jerry’s Sounds Cool thermoacoustic refrigeration system. (Pennsylvania
State University) ..................................................................................................................... 3 Figure 3. (Right) The Space Thermo Acoustic Refrigerator design that was installed on space
shuttle STS-42. (Garrett and Hofler 1991).............................................................................. 3 Figure 4. Computer simulation of a standing wave system in fundamental frequency, where
central cross section of a long resonator is shown with lines indicating the movement of gas
elements, and plots of velocity and pressure distribution. ...................................................... 8 Figure 5. Computer simulation of an air parcel’s location between one set of stack plates in the
stack placed between pressure node and velocity node. ......................................................... 9 Figure 6. Computer simulation of the pressure, volume, temperature of the gas parcel ................ 9 Figure 7. Computer simulation of the pressure, volume, temperature of the gas parcel at the
leftmost position of the gas parcel. ...................................................................................... 10 Figure 8. Computer simulation of the pressure, volume, temperature of the gas parcel moving
from the leftmost position to the rightmost position. ............................................................ 11 Figure 9. Computer simulation of the pressure, volume, temperature of the gas parcel at the
rightmost position of the gas parcel. .................................................................................... 12 Figure 10. An overview of the thermoacoustic refrigeration cycle. (Russell and Weibull 2002) 12 Figure 11. Schematic illustration of the complete set up of the experiment................................. 18 Figure 12. Complete set up of the experiment. View from the inside of practise room 1. ........... 19 Figure 13. Standing wave pattern for 1st, 2nd harmonic in a string fixed at both ends. (San
Francisco State University 2015) .......................................................................................... 20 Figure 14. Cross section of spiral stack structure design. (Russell and Weibull 2002) ................ 22 Figure 15. The surface temperature of diaphragm is measured over 900 seconds. ...................... 25 Figure 16. Loudspeaker’s diaphragm temperature with high amplitude and room temperature
during 900 seconds interval. ................................................................................................. 25 Figure 17. Temperature difference across stack when placed 4.0 ± 0.1 cm vs 9.0 ± 0.1 cm away
from tube opening under fundamental frequencies with high amplitude during 900 seconds
interval. ................................................................................................................................. 26 Figure 18. Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube
opening under fundamental frequencies with various amplitudes during 900 seconds
interval. ................................................................................................................................. 27 Figure 19. Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube
opening under various resonance frequencies with high amplitude during 900 seconds
interval. ................................................................................................................................. 28 Figure 20. (Left) Assembled temperature probes in the straw. ..................................................... 36 Figure 21. (Middle) The mylar strip with fishing wire sewed. ..................................................... 36 Figure 22. (Right). Measuring the width of the rolled stack. ........................................................ 36 Figure 23. Stack from side view (left) and top view (right). ........................................................ 37 Figure 24. Structure of thermoacoustic system with labels of each parts. .................................... 37 Figure 25. Assembled thermoacoustic system. ............................................................................. 39 Figure 26. Structure of configuration system with names with each system................................ 39
iv
Figure 27. An assembled configuration system connected to the thermoacoustic unit while
running and producing a standing wave. .............................................................................. 41 Figure 28. (Left) The three different level of intensity (labelled and max). ................................. 41 Figure 29. (Middle and Right) Measurement of loudspeaker’s current, voltage, loudness under
different amplitude settings. .................................................................................................. 41 Figure 30. Testing environment set up of the experiment. ........................................................... 42 Figure 31. Testing set up in one music practice room, observed outside the acoustically-insulated
glass door. ............................................................................................................................. 43 Figure 32. Web interface that accesses the live stream from the smartphone footage containing
temperature readings in the testing room. ............................................................................. 44
v
List of Tables
Table 1. Summary of the gas parcel’s behaviour during the thermoacoustic refrigeration cycle. 13 Table 2. Experiments performed with various settings. ............................................................... 23 Table D.1 Loudspeaker’s current, potential difference, sound level in three settings. ................. 46 Table E.1 Temperature across stack when placed 4.0 ± 0.1 cm away from tube opening under
fundamental frequency with high amplitude during 900 seconds interval (1.1) .................. 47 Table E.2 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with high amplitude during 900 seconds interval (1.2.1) ............... 47 Table E.3 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with high amplitude during 900 seconds interval (1.2.2) ............... 48 Table E.4 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with high amplitude during 900 seconds interval (1.2.3) ............... 49 Table E.5 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with medium amplitude during 900 seconds interval (2.1.1) ......... 49 Table E.6 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with medium amplitude during 900 seconds interval (2.1.2) ......... 50 Table E.7 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with medium amplitude during 900 seconds interval (2.1.3) ......... 51 Table E.8 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with low amplitude during 900 seconds interval (2.2.1)................. 51 Table E.9 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with low amplitude during 900 seconds interval (2.2.2)................. 52 Table E.10 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
fundamental frequency with low amplitude during 900 seconds interval (2.2.3)................ 53 Table E.11 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening under
2rd harmonic frequency with high amplitude during 900 seconds interval (3.1) ................. 54 Table E.12 Loudspeaker temperature (inside, outside) during 900 seconds interval (4) ............. 54
1
Introduction
Chemical refrigerants have caused tremendous negative environmental impact and there
is no mature replacement. (Bansal et al. 2012) However, the research in thermoacoustics and its
applications in refrigeration provide a new solution with its ability to move heat with acoustic
power. One factor restricting the implementation of thermoacoustic refrigerators is their noise
and it would be useful to investigate the relationship between the intensity and amount of heat
moved, thus to make the system more efficient with less noise. This investigation discusses the
impact of change in acoustic intensity on the amount of heat moved in standing wave
thermoacoustic refrigerators; The investigation particularly focuses on the amplitude and
frequency of the acoustic driver.
Various literatures on the theory and the applications of such systems are reviewed and a
general overview of the topic is discussed. Theories are proposed to demonstrate the working
principles of thermoacoustic refrigeration and the effect of change in intensity. Experiments are
conducted in a high school laboratory environment to prove each hypothesis and results are
evaluated.
2
Investigation
Background
Thermoacoustics Effect
Thermoacoustics is the study of the interaction between heat and sound. The
phenomenon has been observed by glassblowers as they sometimes hear heated vessels generate
tones. (Garrett and Backhaus 2000) The thermodynamic and fluid-dynamic processes of sound
waves in gases can convert energy from one form to another. High-temperature heat can be
partially converted to acoustic power, acoustic power can produce heat, and acoustic power can
pump heat from a low temperature to a high temperature. (Swift 2007)
Standing Wave Thermoacoustic Refrigerators
In a refrigerator or heat pump, externally applied work transfers heat from the lower
temperature reservoir to the higher temperature reservoir. (Russell and Weibull 2002) A standing
wave thermoacoustic refrigerator provides the work to pump heat by standing wave. Dry air and
inert gases (helium, argon) are usually used and the system consists of heat exchangers, an
acoustic driver, a stack, and a resonator (shown in Figure 1).
Figure 1. Schematic illustration of the standing wave thermoacoustic refrigerator with an
acoustic driver. (Kajurek et al. 2017)
3
Standing pressure waves are generated by the driver and cause gas in the resonator to
oscillate forward and backward. A stack of parallel plates is placed inside the resonator between
pressure and velocity node and the gas transports heat when oscillating from one end of the stack
to the other end. The gas near the pressure node gets cooled due to rarefaction and picks up heat
from the stack making one end of stack colder, then moves towards pressure antinode and gets
heated up due to compression. It loses heat to the stack and makes the other end of stack hot.
Thus, a temperature gradient is set up along the stack length and could be used to produce
refrigeration with heat exchangers added at the two ends of the stack. (Dhuley and Atrey 2016)
See theory section for more details.
Most thermoacoustic refrigeration systems and theories have been developed in
laboratories, including Los Alamos National Laboratory, Naval Postgraduate School, and
Pennsylvania State University. They have been mostly deployed to environment where
refrigerant-based refrigerators cannot operate, such as space shuttles (Garrett and Hofler 1991)
and destroyers (Pennsylvania State University), or as a proof of concept for alternative methods
of refrigeration (Pennsylvania State University).
Figure 2. (Left) Ben & Jerry’s Sounds Cool thermoacoustic refrigeration system.
(Pennsylvania State University)
Figure 3. (Right) The Space Thermo Acoustic Refrigerator design that was installed on
space shuttle STS-42. (Garrett and Hofler 1991)
4
Concepts
Standing Longitudinal Wave
In a longitudinal wave, the displacement of the medium is parallel to the propagation of the
wave. When a reflected wave interferes constructively with the incident wave, a standing wave is
formed. (Georgia State University 2016a)
Sound Intensity
Sound intensity or acoustic intensity is the sound power per unit area, with unit of watts per
square meter. It is the rate at which sound energy passes through a unit area held perpendicular to
the direction of propagation of sound waves. (Georgia State University 2016b)
The intensity of the sound can be expressed as
𝐼 = 2𝜋2𝜌𝑓2𝑣∆𝑥2
where I is intensity, ρ is density of the air, f is frequency, v is wave speed, Δx is the change in displacement. (Elert
2016)
Thermal Penetration Depth
Thermal penetration depth is the distance over which the diffusion of heat to or from an adjacent
solid can take place. Its value depends on the frequency of the passing sound wave and
properties of the gas. In typical thermoacoustic devices, and for sound waves in air at audio
frequencies, the thermal penetration depth is typically on the order of one-tenth of a millimeter.
(Garrett and Backhaus 2000)
Isothermal Process
In an isothermal process, temperature remains constant and the product of pressure and volume
is constant. This typically occurs when a system is in contact with an outside thermal reservoir
5
and the change occurs slowly enough to allow the system to continually adjust to reservoir’s
temperature through heat exchange. (Georgia State University 2016c)
Adiabatic Process
In an adiabatic process, energy is transferred to its surroundings only as work without transfer of
heat between the system and its surroundings. In an adiabatic compression, work is done on gas
and its temperature increases; in an adiabatic expansion, the gas does work and its temperature
drops. (Urone and Hinrichs 2018)
Polytropic Process
For an ideal gas in a thermodynamic process:
𝑝𝑉𝑛 = 𝐶
where p is the pressure, V is volume, n is the polytropic index, and C is a constant. (The McGraw-Hill Companies
1998)
In a reversible adiabatic process, the air has a polytropic index of n = 1.4. (Georgia State
University 2016d)
Thus, when pressure increases in an adiabatic process (compression), the volume of air
decreases; when pressure decreases in an adiabatic process (expansion), the volume of air
increases.
Isobaric Process
In an isobaric process, the gas does work while pressure remains constant; the force exerted is
constant and the work done is given as PΔV. (Lumen Learning)
Temperature Gradient
The temperature gradient is the change of temperature with depth. (Russell and Weibull 2002)
6
Work-Energy Principle
The change in the kinetic energy of an object is equal to the net work done on it. (The University
of Winnipeg 1997)
Ideal Gas
For a gas to be “ideal” the gas particles are equally sized and have no inter-molecular forces,
have negligible volume, random motion, and perfect elastic collisions with no energy loss.
(Tenny and Cooper 2018)
7
Hypothesis
The investigation focuses on evaluating the following statements:
1. A thermoacoustic effect can be generated through appropriate design of resonator,
loudspeaker, and stack. A temperature difference across stack will be observed and increase
as time increases.
2. The temperature difference increases when the amplitude of the acoustic driver increases.
3. The temperature difference increases when the harmonic number (resonance frequency) of
the standing wave increases.
A theoretical evaluation would be investigated for each hypothesis, followed by data
analysis of an experiment designed to evaluate the statement.
Theory
Assumptions
Several assumptions are made for this investigation:
1. Viscosity is neglected.
2. Assume air is an ideal gas.
3. Air particles are evenly distributed before the standing wave is formed.
The Pressure-Velocity Distribution of Particles in a Standing Longitudinal Wave
As shown in Figure 4, when a standing wave in an air column with an acoustic source
from the right is formed, the pressure and velocity of the gas particles both oscillate with respect
to time and vary by position. They can be described as a sine function and they oscillate 90º out
of phase. The pressure anti-node is velocity node, and the pressure node is the velocity antinode.
8
Closer to the rarefaction (lowest pressure), the particles move faster; closer to the compression
(highest pressure), the particles move slower.
Figure 4. Computer simulation of a standing wave system in fundamental frequency, where
central cross section of a long resonator is shown with lines indicating the movement of gas
elements, and plots of velocity and pressure distribution.1
Temperature Difference due to Thermoacoustic Effect
A stack is put between the velocity node and the pressure node. The stack is a set of
parallel solid plates creating multiple channels. Imagine a gas parcel with constant amount of air
particles between one pair of the stack plates (shown in Figure 5); it will oscillate between left
(pressure antinode) and right (pressure node) due to the standing longitudinal wave produced.
1 Screenshotted from frame 1 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014).
9
Figure 5. Computer simulation of an air parcel’s location between one set of stack plates in
the stack placed between pressure node and velocity node.2
The behaviour of the gas parcel can be summarized into four stages:
1. As shown in Figure 6, from the right to left end of the stack (from pressure node towards
antinode): The gas parcel undergoes adiabatic compression from low pressure to high
pressure, where work is being done on it as it reduces in volume. According to the work-
energy principle, work being done on the gas increases its kinetic energy, which increases
its temperature as temperature is the measurement of the average kinetic energy.
Figure 6. Computer simulation of the pressure, volume, temperature of the gas parcel
moving from the rightmost position to the leftmost position.3
2 Screenshotted from frame 4 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014). 3 Screenshotted from frame 7 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014).
10
2. As shown in Figure 7, at the left end (closest to pressure antinode) of the stack: The gas
packet now has a higher temperature than the stack (stack’s temperature is represented by
the temperature gradient in the temperature vs location graph), creating a temperature
difference, thus heat is transferred isobarically from the gas parcel to the stack.
Figure 7. Computer simulation of the pressure, volume, temperature of the gas parcel at the
leftmost position of the gas parcel. 4
4 Screenshotted from frame 7 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014).
11
3. As shown in Figure 8, from the left to right end of the stack (from pressure antinode
towards node): The gas parcel undergoes adiabatic expansion from high pressure to low
pressure, where it does work on the surrounding as it increases in volume. According to
the work-energy principle, gas does work thus its kinetic energy decreases, and
temperature also decreases as temperature is the measurement of the average kinetic
energy.
Figure 8. Computer simulation of the pressure, volume, temperature of the gas parcel
moving from the leftmost position to the rightmost position.5
5 Screenshotted from frame 7 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014).
12
4. As shown in Figure 9, at the right end (closest to pressure node) of the stack: The gas
packet now has a lower temperature than the stack (stack’s temperature is represented by
the temperature gradient in the temperature vs location graph), creating a temperature
difference, thus heat is transferred isobarically from the stack to the gas parcel.
Figure 9. Computer simulation of the pressure, volume, temperature of the gas parcel at the
rightmost position of the gas parcel. 6
Figure 10. An overview of the thermoacoustic refrigeration cycle. (Russell and Weibull
2002)
6 Screenshotted from frame 7 of the standing-wave thermoacoustic engine or refrigerator animation program in
computer animations produced by Swift and Ward (2014).
13
Stage /
location of
gas parcel
Volume of
gas parcel
Pressure of
gas parcel
Temperature
of gas parcel
Flow of heat between gas parcel and
stack plate
From right to
left
Decreasing Increasing Increasing Transition from stack plate to gas parcel
to from gas parcel to stack
Leftmost
position
Minimum Maximum Maximum From gas parcel to stack
From left to
right
Increasing Decreasing Decreasing Transition from gas parcel to stack to
from stack plate to gas parcel
Rightmost
position
Maximum Minimum Minimum From stack plate to gas parcel
Table 1. Summary of the gas parcel’s behaviour during the thermoacoustic refrigeration
cycle.
Figure 10 and Table 1 summarize the thermodynamic cycle of the four stages. By
repeating the cycle, the gas parcel takes in heat from stack at the right-most position and rejects
heat to the stack at the left-most position. This process applies to all gas parcels in the stack and
results in a net effect of small amount of heat being moved a short distance along the stack from
the colder end towards the hotter end; a temperature gradient is thus created, with stack’s
temperature increases from the cold end to the hot end continuously due to the thermodynamic
process performed by gas parcels. Overall, heat is being transferred from the right side of the
stack to the left side and temperature difference between gas on both sides is created.
Note that the temperature vs position time graph has an area enclosed. This is due to the
thermal contact between the gas parcel and the stack plate (Swift and Ward 2014). During
processes 1 and 3, most of the gas parcel undergoes adiabatic compression and expansion
respectively, particularly the center of the gas parcel that is distant from the plate. The other part
of the gas parcel contacting the plate is compressed and expanded isothermally. The distance of
gas parcel particles maintaining a good thermal contact with the plate is about one thermal
penetration depth from the plate. (Kajurek et al. 2017) This distance is crucial to decide the
14
spacing between stack plates in order to support both adiabatic and isothermic process to take
place.
The area enclosed by the circle in the P-V diagram represents the amount of work used to
pump heat across stack.
The Effect of Amplitude Changes
When the acoustic driver becomes louder, the sound intensity (I) increases. The standing
wave created from the resultant interference of the generated and reflected longitudinal now has
a larger sound intensity overall and becomes larger in amplitude. According to the intensity–
pressure equation (Elert 2016)
𝐼 = ∆𝑃2
2𝜌𝑣
Where I is intensity, ∆P is pressure amplitude, ρ is density of the air, and v is wave speed.
However, the density and wave speed are constant; As an entire system, the air particles still
have the same density regardless of their distributions as a result of standing wave and they
follow the speed of sound because medium is unchanged.
Thus, 𝐼 ∝ 𝑃𝟐
When the intensity of the sound increases, the average amplitude of the pressure
distributions increases. The cosine function of pressure shown in Figure 4 is now increased in
amplitude. However, the increase in amplitude of the pressure distribution does not necessarily
prove the change in amplitude of velocity distribution with equation of 𝑝𝑉𝑛 = 𝐶; Constant C can
also change. Its impact on velocity must be understood in dynamics.
15
Recall the air parcel in Figure 5. The pressure exerted on the parcel from the left (closer
to pressure antinode) is greater than the pressure exerted on the parcel from the right (closer to
pressure node). The definition of pressure is that:
𝑃 =𝐹
𝐴
Where P is pressure, F is the force, A is the area that the force is exerted on.
Since the area of the air parcel contacting the other air particles on both side is the same
(same height), the force exerted on the parcel from the left is larger than the force exerted from
the right. Thus, a net force is created pointing to the right. The net force would increase as the
magnitude of both forces increase, as a result of the pressure increase on both side from the
increase in acoustic intensity.
According to Newton’s second law: 𝐹𝑛𝑒𝑡 = 𝑚𝑎, since the mass of the parcel is constant
(same number of air particles in parcel), thus the acceleration is directly proportional to the net
force. When the net force increases, the acceleration of the air parcel as well as the air particles
increase. Since the frequency stays constant, the time period (Δt) of the air to oscillate does not
change. According to kinematics equation: ∆𝑣 = 𝑎∆𝑡, as acceleration increases, the change in
velocity also increases. Again, according to kinematics equation: ∆𝑑 =𝑢+𝑣
2∆𝑡, the change in
velocity increases the distance that the air parcel molecules travel. Each air particle in the parcel
has a different velocity due to the standing wave velocity distribution, so the distance they travel
varies. The net length of the parcel is the difference of the distance travelled of each particle, and
thus increases when the distance travelled of each particle is increased. Since the volume of the
parcel is 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ × ℎ𝑒𝑖𝑔ℎ𝑡, and height and width are constant as it is in a uniform
channel, the change in volume of the parcel increases as the change in length increases.
16
To conclude, as intensity increases, the change in volume of air parcel increases. Thus,
during adiabatic expansion/compression, the amount of work that the air parcel exerted/was
exerted upon increases, thus the change in kinetic energy increases. Temperature is a
measurement of average kinetic energy, and the temperature on the left would increase more
because more kinetic energy is being added, and the temperature on the right would decrease
more because more kinetic energy is lost. Thus, with increased acoustic intensity, the
temperature difference across stack and the amount of heat moved is increased.
The Effect of Frequency Changes
Imagine in a standing wave thermoacoustic system, the resonance frequency is changed
from fundamental to second harmonic. Assume the stack is adjusted in length thus the pressures
at the ends of stack in second harmonic are the same as the pressures at the ends of the original
stack in first harmonic. As the resonance frequency (or harmonic number) increases, the period
of oscillations decreases. Thus, in a given amount of time, more thermodynamic cycle can be
repeated, more heat can be transferred, and a greater temperature difference would be formed
across stack. This effect can also be understood from change in intensity. According to the
intensity equation
𝐼 = 2𝜋2𝜌𝑓2𝑣∆𝑥2, Thus, 𝐼 ∝ 𝑓𝟐
As the frequency increases, the intensity increases. Using the conclusion from the
previous investigation on sound intensity’s effect on the temperature change, it can be concluded
that as harmonic frequencies increases, acoustic intensity increases, more heat is moved and the
temperature difference across stack increases.
17
Experiment
Objective
An experiment is designed to prove the hypothesis by:
1. Demonstrating the thermoacoustic effect with a standing wave thermoacoustic
refrigerator.
2. Investigating the relationship between change in intensity of sound (amplitude of
speaker) and temperature difference.
3. Investigating the relationship between standing wave harmonic frequencies and
temperature difference.
A thermoacoustic refrigeration is designed and built with the following functionalities.
1. Include all components of a standing wave thermoacoustic refrigerator.
2. Produce a fixed-end standing wave pattern with a loudspeaker.
3. Configure the loudspeaker’s frequency and amplitude.
4. Able to measure temperature difference across the stack
The experiment is practical because at the auditory threshold of pain (120 dB) in standard
atmosphere pressure, temperature oscillates up and down by about 0.02°C. (Garrett and
Backhaus 2000) Although this is a small difference, it can cumulate over a period of time and
thus demonstrate some amount of heat is being moved across stack and show a temperature
difference that is detectable by the digital temperature probes.
18
Brief Description of Experiment Design
Figure 11. Schematic illustration of the complete set up of the experiment.
As shown in Figure 11, the set up contains a thermoacoustic unit and a configuration
system in a testing environment. The thermoacoustic unit resembles a thermoacoustic heat pump
with a test tube (1) as resonator, a stack with temperature probes (2), and a loudspeaker (3). They
are enclosed in a clear case (4) to prevent the possible flying glass pieces if the resonating test
tube breaks. The configuration system includes a frequency generator (5) that is connected to the
loudspeaker to configure the amplitude and frequency. A microphone (6) is placed underneath
the tube to detect the presence of resonance with an oscilloscope (7). While attempts were made
to use a small microphone to detect pressure distributions inside the tube, the microphone is the
most tangible way to detect resonance and presence of standing wave. The temperature probes in
the stack (2) are connected to two temperature guns (8) with digital displays, and the readings are
livestreamed through a smartphone (9) over server (10) to a laptop in another isolated room (11)
to avoid the researcher to be directly exposed to high volume environment. Figure 12 shows a
complete set up of the experiment inside practise room 1.
19
Figure 12. Complete set up of the experiment. View from the inside of practise room 1.
Detailed list of materials and procedures of the constructions of the system can be found in
Appendix A and B respectively.
Standing wave pattern
A standing longitudinal wave pattern is created to generate the constant pressure
variations. The frequency of the standing wave has been calculated and being inputted in a
frequency generator. This experiment uses a pipe closed at both ends, which behaves similar to a
string fixed at both ends. There is a displacement node at each end when a standing wave is
formed. (Brown 2004)
𝐿𝑡𝑢𝑏𝑒 = 14.8 ± 0.1 cm = 0.148 ± 0.001 m
𝑇𝑟𝑜𝑜𝑚 = 22.0 ± 0.1°C
𝑉𝑠𝑜𝑢𝑛𝑑 = 331 𝑚𝑠−1 + 0.61𝑚𝑠−1°C−1𝑇𝑟𝑜𝑜𝑚 = 331𝑚𝑠−1 + 0.61 × (22.0 ± 0.1°C )
= 334.42 ± 0.061𝑚𝑠−1 ≈ 334.42 ± 0.06𝑚𝑠−1
As Figure 13 shows, the relationship between wavelength and tube length can be calculated:
20
Figure 13. Standing wave pattern for 1st, 2nd harmonic in a string fixed at both ends. (San
Francisco State University 2015)
𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑛𝑡ℎ ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐: 𝜆 = 2𝐿𝑡𝑢𝑏𝑒
𝑛, 𝑛 ∈ ℤ+
𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒 𝑛𝑡ℎ ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐: 𝑓 = 𝑣
𝜆=
𝑣𝑛
2𝐿𝑡𝑢𝑏𝑒=
(344.42 ± 0.06𝑚𝑠−1)𝑛
2 × (0.148 ± 0.001 m), 𝑛 ∈ ℤ+
Thus, frequency f required to generate 1st, 2nd harmonic in the system can be calculated.
∴ 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒 1𝑠𝑡 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐: 𝑓 =(344.2 ± 0.06𝑚𝑠−1) ∗ 1
2 × (0.148 ± 0.001 m)= 1162.8 ± 8.1 Hz
The frequency to generate 1st harmonic is also called the fundamental frequency.
∴ 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒 2𝑛𝑑 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐: 𝑓 =(344.2 ± 0.06𝑚𝑠−1) ∗ 2
2 × (0.148 ± 0.001 m)= 2325.7 ± 16.1 Hz
Stack Design
As described in theory, the stack is essential to the thermoacoustic process. Following
calculations determine the design of stack under fundamental frequency.
Thermal Penetration Depth
Thermal penetration depth δ𝑘 is calculated so the stack spacing will have enough room
for some part of the gas to undergo adiabatic expansion and compression and not being
influenced by the isothermal heat exchange of gas along the stack plate.
21
δ𝑘 = √2𝐾
𝜌𝑚𝐶𝑝𝜔 (Dhuley and Atrey 2016)
Where K / Wm-1K-1 is the thermal conductivity, ρm / kgm-3 is the density, Cp / Jkg-1K -1 is the isobaric specific heat,
ω / rad s-1 is the angular frequency.
𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦7 𝐾 = 26.02 ± 0.03 𝑚𝑊𝑚−1𝑘−1 = 0.02602 ± 0.00003 𝑊𝑚−1𝐾−1
𝐷𝑒𝑛𝑠𝑖𝑡𝑦8 𝜌𝑚 = 1.196 ± 0.0002392 𝑘𝑔𝑚−3
𝐼𝑠𝑜𝑏𝑎𝑟𝑖𝑐 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐 ℎ𝑒𝑎𝑡9 𝐶𝑝 = 1.005 ± 0.001 𝑘𝐽𝑘𝑔−1𝐾−1 = 0.001005 ±
0.000001 𝐽𝑘𝑔−1𝐾−1
𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝜔 = 2𝜋𝑓 = 2𝜋(1162.8 ± 8.1 Hz) = 7306.09 ± 50.89Hz
∴ δ𝑘 = √2𝐾
𝜌𝑚𝐶𝑝𝜔
= √2(0.02602 ± 0.00003 𝑊𝑚−1𝐾−1)
(1.196 ± 0.0002392 𝑘𝑔𝑚−3)( 0.001005 ± 0.000001 𝐽𝑘𝑔−1𝐾−1)(7306.09 ± 50.89Hz)
δ𝑘 = 7.670 × 10−5 ± 3.571 × 10−7 = 0.07670 ± 0.0003571𝑚𝑚
The optimal spacing h between stack is 4 times the thermal penetration depth (Swift 1995)
ℎ = 4δ𝑘 = 4 × (0.07670 ± 0.0003571𝑚𝑚) = 0.3068 ± 0.001428𝑚𝑚 ≈ 0.3𝑚𝑚
Blockage Ratio
The blockage ratio is the ratio of area available to gas in the stack to the total area of the
stack. (Putra and Agustina 2013) The ideal blockage ratio is characterized as:
Br = h
h+t= 0.75 (Tijani et al. 2002)
Where h is the spacing between stack, and t is the stack plate’s thickness.
∵ h = 0.3 mm ∴ t = 0.1mm
7 The K value is calculated under standard atmospheric pressure at 22 °C with 0.1% uncertainties.
(Engineering ToolBox) 8 The ρ𝑚value is calculated under standard atmospheric pressure at 22 °C with 0.2% uncertainties.
(Engineering ToolBox) 9 The C𝑝value is calculated under standard atmospheric pressure at 300K with 1% uncertainties. (Urieli 2008)
22
Geometry of the Stack
It is hard to create a parallel plate system without precise machineries. Instead, a spiral
structure similar to Figure 14 is used, where rolled mylar paper strip is used to create stack walls
and fishing lines are used to guaranteed the constant spacing between walls.
Figure 14. Cross section of spiral stack structure design. (Russell and Weibull 2002)
Mylar is chosen for its low thermal conductivity to minimize the losses caused by the
ordinary heat conduction along the temperature gradient. (Kajurek et al. 2017). Chosen by the h,
t value calculated, the mylar paper used is approximately 0.1 mm thick and the fishing line is
exactly 0.3 mm thick, guaranteeing the accuracy of the stack. Two temperature probes are
installed in the stack facing left and right.
Stack Placement
The stack was placed between a pressure antinode and pressure node. In a fundamental
standing wave system, there are two possible locations satisfying such condition: between the
antinode on the left and the node in the middle, and between the node in the middle and the
antinode on the right. The stack was placed in two locations during the experiment, at 4.0 ±
0.1 𝑐𝑚 (location 1) and 9.0 ± 0.1 𝑐𝑚 (location 2) away from the acoustic driver.
23
Experiments Conducted
A series of experiments are conducted to evaluate the hypothesis. The thermoacoustic
units are given various configurations (amplitude, frequency of sound, stack location) to form
standing wave and the data of the temperature probes at the left end (T1) and right end (T2) of
stack is taken in 60 seconds interval for 15 minutes. Some experiments are repeated 3 times to
reduce errors. Table 2 specifies all experiments performed.
Experiment Number Loudspeaker
Amplitude10
Frequency11 Stack Location (distance
away from loudspeaker)
Experiment 1: The presence of thermoacoustic effect
1.1 High Fundamental Location 1 (4.0 ± 0.1 cm)
1.2.1 High Fundamental Location 2 (9.0 ± 0.1 cm)
1.2.2 High Fundamental Location 2 (9.0 ± 0.1 cm)
1.2.3 High Fundamental Location 2 (9.0 ± 0.1 cm)
Experiment 2: Relationship between amplitude of speaker and temperature difference
2.1.1 Medium Fundamental Location 2 (9.0 ± 0.1 cm)
2.1.2 Medium Fundamental Location 2 (9.0 ± 0.1 cm)
2.1.3 Medium Fundamental Location 2 (9.0 ± 0.1 cm)
2.2.1 Low Fundamental Location 2 (9.0 ± 0.1 cm)
2.2.2 Low Fundamental Location 2 (9.0 ± 0.1 cm)
2.2.3 Low Fundamental Location 2 (9.0 ± 0.1 cm)
Experiment 3: Relationship between the resonance frequency and temperature difference
3.1 High Second Harmonic Location 2 (9.0 ± 0.1 cm)
Table 2. Experiments performed with various settings.
Environment data and detailed operations of the experiment can be found in Appendix C
and D respectively. Appendix E contains all raw data.
10 The various amplitude settings (current, potential difference, loudness) can be found in Appendix C. 11 The frequencies are frequencies calculated in the standing wave pattern section.
24
Analysis of Data
Error Sources
Inaccuracy caused by Instruments and Methods
1. Temperature Probe: The temperature probes take the average reading of air
temperature along themselves. However, the probes do not directly measure the stack
temperature, and the volume (and thus mass) of air left and right to the stack are
different, which would result one temperature rising faster due to less mass. There is
also time delay in updating data and a significant uncertainty.
2. Standing Wave: The tube bottom is not flat thus it influences the ideal frequency
calculated. Using microphone to detect resonance is not ideal and identified
resonance frequencies might not be accurate.
3. Stack: Although the stack has constant spacings in theory by the separation of fishing
lines, there might be uneven or extra spacings while stack is rolled, influencing the
thermal penetration depth and the thermodynamics processes.
4. Heat Process: The heat gained or lost can be absorbed and added by the tube to reach
equilibrium with environment, thus reducing the value of temperature changes.
Heating Effect of the Loudspeaker
Loudspeaker also generates heat and Experiment 4 was performed to measure
diaphragm’s surface temperature, as shown in Figure 15. As shown in Figure 16, the
diaphragm’s temperature rises rapidly. The radiation it creates can add a significant amount of
heat to the air in tube. T2 has a higher temperature rise than T1 because it’s closer to the
25
loudspeaker, but both value rise (shown in all data) showing that radiation can be a significant
error source. The diaphragm is also directly heating the air in the tube by thermal conduction.
Figure 15. The surface temperature of diaphragm is measured over 900 seconds.
Figure 16. Loudspeaker’s diaphragm temperature with high amplitude and room
temperature during 900 seconds interval.12
12 Raw data can be found in Table E.12.
0
10
20
30
40
50
60
70
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900
Tem
pe
ratu
re T
/ °
C (
±0.
1 °C
)
Time t / s (± 0.1 s)
Loudspeaker's diaphragm temperature with high amplitude and room temperatrure during 900 seconds interval
Room Temperature Diaphragm Temperature
26
Evaluation of Experiments
Thermoacoustic Effect (Experiment 1)
Figure 17. Temperature difference across stack when placed 4.0 ± 0.1 cm vs 9.0 ± 0.1 cm
away from tube opening under fundamental frequencies with high amplitude during 900
seconds interval.13
When stack is placed in location 1 (1.1), the pressure antinode is on the right, thus
temperature would be higher on the right and ΔT would be positive. Although the results align
with this and show the difference also increases over time (shown in Figure 17), a 9°C
temperature rise seems much higher than the cumulative temperature change that the system can
produce. In fact, the right probe increases temperature rapidly due to its proximity to the speaker.
The stack is then moved to location 2 (1.2.1-3) for further experiments, and the effect of
radiation is much reduced when moved further away. ΔT is supposed to be negative because T1
is closer to the pressure antinode on the left now. However, the data is positive. T2 is closer to
13 Raw data can be found in Table E.1-4.
-1
0
1
2
3
4
5
6
7
8
9
-100 0 100 200 300 400 500 600 700 800 900 1000
Tem
pe
ratu
re d
iffe
ren
ce b
etw
een
air
to
th
e ri
ght
and
left
of
stac
k Δ
T =
T2 –
T1 /
°C
(±
0.2
°C)
Time t / s (± 0.1 s)
Temperature difference across stack when placed 4.0 ± 0.1 cm vs 9.0 ± 0.1 cm away from tube opening under fundamental frequencies
with high amplitude during 900 seconds interval
1.2.1 1.2.2 1.2.3 1.1
27
loudspeaker thus the result of radiation and air conduction might have entirely outweighed the
thermoacoustic effect created. Thus, the presence of thermoacoustic effect that is supposed to
happen by design cannot be concluded due to the significant error sources.
Effect of Amplitude change (Experiment 2)
Figure 18. Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube
opening under fundamental frequencies with various amplitudes during 900 seconds
interval.14
As shown in Figure 18, temperature differences ΔT has a larger amplitude when
loudspeaker’s amplitude increases. However, the sign of theoretical ΔT is completely opposite to
14 Raw data can be found in Table E.2-10.
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 100 200 300 400 500 600 700 800 900
Tem
per
atu
re d
iffe
ren
ce b
etw
een
air
to
th
e ri
ght
and
left
of
stac
k Δ
T =
T2 –
T1 /
°C
(±
0.2
°C)
Time t / s (± 0.1 s)
Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube opening under fundamental frequencies with
various amplitudes during 900 seconds interval
1.2.1 1.2.2 1.2.3 2.1.1 2.1.2 2.1.3 2.2.1 2.2.2 2.2.3
28
the data collected as described before, and the amplitude effect cannot be supported by the data
collected. The increased ΔT can be resulted from increased heating of loudspeaker when
amplitude increases. The thermoacoustic effect might have increased but the radiation and
conduction of loudspeaker heat completely outweigh it.
Effect of Frequency change (Experiment 3)
Figure 19. Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube
opening under various resonance frequencies with high amplitude during 900 seconds
interval.15
The experiment data and trend shown in Figure 19 cannot prove the frequency effect because:
1. The stack length was not reduced when switching to second harmonic (3.1) thus pressure
at ends of stacks are different than before, making the results incomparable.
15 Raw data can be found in Table E.2-4, E.11.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 200 400 600 800 1000
Tem
pe
ratu
re d
iffe
ren
ce b
etw
een
air
to
th
e ri
ght
and
left
of
stac
k Δ
T =
T2 –
T1 /
°C
(±
0.2
°C)
Time t / s (± 0.1 s)
Temperature difference across stack when placed 4.0 ± 0.1 cm away from tube opening under various resonance frequencies with
high amplitude during 900 seconds interval
1.2.1 1.2.2 1.2.3 3.1
29
2. The unreduced length does not satisfy the setting of stack being placed a node and
antinode anymore because more nodes and antinodes are created now and the stack rests
in regions of both increasing and decreasing pressure.
3. The loudspeaker broke down after one run in second harmonic, thus the results are
inconclusive. However, the data all shows an increasing ΔT as a result of the
loudspeaker’s heating effect.
30
Conclusion
Evaluation
This investigation demonstrated the theory of thermoacoustic refrigeration in standing
wave system, the theoretical effect of sound intensity, particularly with amplitude and frequency,
and an attempt to prove the theories experimentally. The amount of heat moved was investigated
indirectly by measuring the temperature difference across stack. While the theory cannot be
supported by the data due to various possible error sources, it was analyzed clearly with high
school physics knowledge.
Thermoacoustic refrigeration systems have unique advantages as they are reliable (one
moving part), environmentally friendly (no chemicals), and cost-efficient (electric-powered).
Further investigations on the effect of intensity can help establish design guidelines for specific
refrigeration goals and improve efficiency of such systems.
Areas of Improvements
1. Reduce speaker coil temperature with a larger loudspeaker.
2. Use a loudspeaker with higher sound level and power.
3. Use a 3D-printed stack that is more uniform and accurate.
4. Use a more sensitive temperature probe.
5. The Prandtl number of dry air is around 0.7. The efficiency can be increased by using
gas mixtures with Prandtl below 2
3 , such as helium. (Starr et al. 1996)
6. Use silicone sealant to reduce acoustic escape.
31
References
Bansal P, Vineyard E, Abdelaziz O. 2012. Status of not-in-kind refrigeration technologies for
household space conditioning, water heating and food refrigeration. International Journal of
Sustainable Built Environment. 1:85–101. doi:10.1016/j.ijsbe.2012.07.003.
Brown RG. 2004. Pipe Closed at Both Ends. [accessed 2018 May 23].
https://webhome.phy.duke.edu/~rgb/Class/phy51/phy51/node47.html.
Dhuley RC, Atrey MD. 2016. Design Guidelines For a Thermoacoustic Refrigerator.
arXiv:160105149 [physics]. [accessed 2018 Apr 4]. http://arxiv.org/abs/1601.05149.
Elert G. 2016. Intensity – The Physics Hypertextbook. [accessed 2018 May 23].
https://physics.info/intensity/.
Engineering ToolBox. Air - Thermal Conductivity. [accessed 2018a May 23].
https://www.engineeringtoolbox.com/air-properties-viscosity-conductivity-heat-capacity-
d_1509.html.
Engineering ToolBox. Air - Density, Specific Weight and Thermal Expansion Coefficient at
Varying Temperature and Constant Pressures. [accessed 2018b May 24].
https://www.engineeringtoolbox.com/air-density-specific-weight-d_600.html.
Garrett SL, Backhaus S. 2000. The Power of Sound. :11.
Garrett SL, Hofler TJ. 1991. Thermoacoustic Refrigeration.
Georgia State University. 2016a. Standing Waves. [accessed 2018 May 24].
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/standw.html.
Georgia State University. 2016b. Sound Intensity. [accessed 2018 May 24].
http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/intens.html.
Georgia State University. 2016c. Isothermal Processes. [accessed 2018 May 21].
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html#c3.
Georgia State University. 2016d. Adiabatic Processes. [accessed 2018 May 23].
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html.
Kajurek J, Rusowicz A, Grzebielec A. 2017. The Influence of Stack Position and Acoustic
Frequency on the Performance of Thermoacoustic Refrigerator with the Standing Wave.
Archives of Thermodynamics. 38. doi:10.1515/aoter-2017-0026.
Lumen Learning. Ideal Gas Law | Boundless Physics. [accessed 2018 May 23].
https://courses.lumenlearning.com/boundless-physics/chapter/ideal-gas-law/.
32
Pennsylvania State University. SETAC project: Shipboard Electronics Thermoacoustic Chiller -
Thermoacoustic Refrigeration at Penn State. [accessed 2018a May 21].
http://www.acs.psu.edu/thermoacoustics/refrigeration/setac.htm.
Pennsylvania State University. SOUNDS COOL! The Ben & Jerry’s Project - Thermoacoustic
Refrigeration at Penn State. [accessed 2018b May 21].
http://www.acs.psu.edu/thermoacoustics/refrigeration/benandjerrys.htm.
Putra N, Agustina D. 2013. Influence of stack plate thickness and voltage input on the
performance of loudspeaker-driven thermoacoustic refrigerator. Journal of Physics: Conference
Series. 423:012050. doi:10.1088/1742-6596/423/1/012050.
Russell D, Weibull P. 2002. Tabletop thermoacoustic refrigerator for demonstration.
San Francisco State University. 2015. Chapter 8. Standing Waves on a String.
Starr R, Bansal PK, Jones RW, Mace BR. 1996. The Reality of a Small Household
Thermoacoustic Refrigerator. :7.
Swift G. 2007. Thermoacoustics. In: Springer Handbook of Acoustics. Springer, New York, NY.
p. 239–255. [accessed 2018 May 21]. https://link.springer.com/referenceworkentry/10.1007/978-
0-387-30425-0_7.
Swift GW. 1995. Thermoacoustic Engines and Refrigerators. Physics Today. 48:22.
doi:10.1063/1.881466.
Swift GW, Ward B. 2014. Educational Animations - Computer animations of thermoacoustic
processes.
Tenny KM, Cooper JS. 2018. Chemistry, Ideal Gas Behavior. In: StatPearls. Treasure Island
(FL): StatPearls Publishing. [accessed 2018 May 21].
http://www.ncbi.nlm.nih.gov/books/NBK441936/.
The McGraw-Hill Companies. 1998. The Polytropic Process. [accessed 2018 May 23].
http://www.mhhe.com/engcs/mech/cengel/notes/ThePolytropicProcess.html.
The University of Winnipeg. 1997. Kinetic Energy and the Work Energy Theorem. [accessed
2018 May 21]. http://theory.uwinnipeg.ca/physics/work/node3.html.
Tijani ME., Zeegers JC., de Waele ATA. 2002. Design of thermoacoustic refrigerators.
Cryogenics. 42:49–57. doi:10.1016/S0011-2275(01)00179-5.
Urieli I. 2008. Specific Heat Capacities of Air. [accessed 2018 Apr 8].
https://www.ohio.edu/mechanical/thermo/property_tables/air/air_Cp_Cv.html.
Urone PP, Hinrichs R. 2018. 3.6: Adiabatic Processes for an Ideal Gas - Physics LibreTexts.
[accessed 2018 May 21].
https://phys.libretexts.org/?title=TextBooks_%26_TextMaps/University_Physics_TextMaps/Ma
33
p:_University_Physics_(OpenStax)/Map:_University_Physics_II_-
_Thermodynamics,_Electricity,_and_Magnetism_(OpenStax)/3:_The_First_Law_of_Thermodyn
amics/3.6:_Adiabatic_Processes_for_an_Ideal_Gas.
34
Appendix A - Materials and Tools
Full List of Materials Used
1 – 2W 8Ω loudspeaker
1 – PYREX borosilicate glass 55mL test tube (length 150 mm, diameter 25 mm)
1 – Graduated cylinder base
10 – 1/8" self-tightening screws
1 – Acrylic stationery drawer
2 – Omega temperature gun with temperature probe
1 – Vernier sound level meter
1 – Vernier gas pressure sensor
1 – Vernier LabQuest Mini
1 – Microphone
1 – Tektronix 2205 20MHz Oscilloscope
1 – Pasco Scientific digital function generator
2 – BNC to alligator cable
4 – Banana cable
4 – Alligator clips
1 – DT830B digital multimeter
2 – Tripods
1 – LG G5 smartphone
Mylar paper
10 lb. fishing line
Green paper tape
35
3M electrical tape
Plastic straw
Plywood
Full List of Tools Used
Safety goggles
Earmuff
Drill press
Hand drill
Band saw machine
Hot glue gun
Scissor
Utility knife
Robertson square head screw driver
Pushpins
Marker
Ruler
Caliper
36
Appendix B - Engineering Procedure
Stack Building
Mylar paper strip with a width of 35 mm is chosen to build the stack wall with an
approximate layer height of 0.1 mm. Holes are punched through push pins throughout the mylar
paper strip, every 10 mm on both side. 10lb fishing lines are used to create the height h, which is
exactly about 0.3 mm thick. Fishing lines are sewed through holes cut and an extra length is
obtained to create a mechanism to retreat the stack. (Figure 20) The mylar strip with fishing line
sewed is then rolled around a plastic straw with pressure from fingers, guaranteeing
approximately constant height about 0.3 mm. (Figure 21) The outside of the rolled mylar is taped
with green paper tape and electric tape to minimize heat exchange with the test tube. As shown
in Figure 19, two temperature probes facing different directions are inserted in the plastic straw,
not blocking any of the wall and heights. Figure 22 demonstrates the stack mechanism built.
Figure 20. (Left) Assembled temperature probes in the straw.
Figure 21. (Middle) The mylar strip with fishing wire sewed.
Figure 22. (Right). Measuring the width of the rolled stack.
37
Figure 23. Stack from side view (left) and top view (right).
Thermoacoustic System
Figure 24. Structure of thermoacoustic system with labels of each parts.
As shown in Figure 24, the thermoacoustic unit is a standalone system that contains
various modular components. Everything is contained in an acrylic stationery drawer (3) that is
missing only one side (bottom side). A circle (d = 25 mm) is carved out on the right wall of the
drawer and a piece of hexagon pinewood (5) and plastic Graduated cylinder base (6) are taped
38
together and drilled onto the left wall of the drawer with 6 1/8" self-tightening screws. A PYREX
test tube (2) is then injected from the hole on the right wall and being held stably with the
graduated cylinder base. The primary function of such design is to securely place the test tube in
a stable location, make add-ons and modifications easily, and prevent any possible breaking test
tube parts from injuring others from possible breakdowns while producing a standing wave
pattern. The tube and case are both transparent thus making it easily observable.
A stack (7), made with mylar paper, fishing wire, 3M electric tape, and green paper tape,
is being shoved into the tube by a screw driver to the appropriate locations which would be
mentioned later. Two temperature probes are extended from the stack to both directions,
measuring air temperature left (8) and right (9) to the stack. The wires of the probes
are wrapped inside a plastic straw tube inside the stack, and the probes are not touching the
walls. The wires (10, 11) carrying data from left and right temperature probe (8 and 9,
respectively) are extended outside the tube opening. Finally, a 2W 8 Ω loudspeaker (1) is
installed at the tube opening on the box panel by four 1/8" self-tightening screws. It enclosed the
tube system, and only allow the two wires carrying temperature data to be extended to the
outside.
A microphone (4) is placed unconnected to the drawer on the ground under the tube
opening. It is used to examine if a standing wave is formed by showing its signals on an
oscilloscope. Figure 25 shows a complete set up of the thermoacoustic system.
39
Figure 25. Assembled thermoacoustic system.
Configuration System
Figure 26. Structure of configuration system with names with each system.
40
As Figure 26 shows, the thermoacoustic unit is then connected to several other systems to
function. The two temperature wires are connected two temperature guns (gun 1, gun 2,
corresponding to the probe left and right to the stack) mounted on a tripod platform, to keep
temperature readings fixed in positions. The cathode and anode of the loudspeaker is connected
to the cathode and anode end of a Pasco Scientific digital function generator through 2 bananas
cable who are clipped on the loudspeakers with alligator clips. The frequency generator is
capable of changing the amplitude, waveform and frequencies of the current outputted. A
Tektronix 2205 20MHz oscilloscope is used to inspect the waveform characteristics of the
current outputted from the frequency generator, as well as the sound produced. Channel one is
connected the cathode and anode of the frequency generator through a BNC to alligator cable, to
examine the signal generated from the generator. Channel two is connected to the cathode and
anode of the microphone (3.5 mm male audio plug), to examine whether a single frequency is
generated for the standing wave and whether a standing wave is formed (when amplitude of
wave shown on oscilloscope reaches maximum). Figure 27 shows an assembled and running
configuration system connected to the thermoacoustic unit while producing a standing wave.
Three different levels of amplitude output were labelled (Figure 28), and the loudness, current,
and potential difference settings for each level are recorded using a sound level sensor and a
digital multimeter (Figure 29).
41
Figure 27. An assembled configuration system connected to the thermoacoustic unit while
running and producing a standing wave.
Figure 28. (Left) The three different level of intensity (labelled and max).
Figure 29. (Middle and Right) Measurement of loudspeaker’s current, voltage, loudness
under different amplitude settings.
42
Testing Environment
Figure 30. Testing environment set up of the experiment.
Because the loudspeaker is continuously generating a soundwave that is above 100 dB
(see Table D.1), and under the high amplitude setting it is approaching 120 dB (human ear pain
level), noise reduction and insulation process are installed to protect researcher. A construction
site level earmuff is used when configuring the machine in close proximity. The system is being
tested in an enclosed music practice room. It has a constant air circulation system and being
underground guaranteed little room temperature changes. The music practice room ensured that
the sound generated from the experiment has minimum effect on others through sound
insulation, and the experiment would not be affected by outside noise. (Figure 30)
The practice room is filled with dry air, and the air pressure P measured from a Vernier
gas pressure sensor connected to a Vernier LabQuest Mini shown in LoggerPro is 98.90 ±
0.01kPa. The room temperature Troom measured from a temperature probe connected to the
temperature gun is 22.0 ± 0.1°C.
In order to minimize contact with high volume and creating any disturbance to the testing
environment, and meanwhile constantly reading the temperature probe data, a livestream system
is put in place. As Figure 31 shows, A LG G5 smartphone hot glued on a tripod is aimed with its
43
back camera towards the temperature gun display screen. The application IP Camera can stream
video footage with negligible delay at a resolution of 1920x1080 pixels towards a cloud server.
As Figure 32 illustrates, the researcher can access the reading real-time on his/her laptop by
accessing a web interface that accesses the footage from the server. The researcher for most of
the duration of the experiment does not need to enter the test room and thus minimize contact
with high volume.
Figure 31. Testing set up in one music practice room, observed outside the acoustically-
insulated glass door.
44
Figure 32. Web interface that accesses the live stream from the smartphone footage
containing temperature readings in the testing room.
45
Appendix C - Operation Procedure
A set of procedures is being performed for each experiment involving the thermoacoustic unit.
1. Insert the stack to appropriate location in the tube using a screw driver, avoid temperature
probes from touching the test tube wall. Seal the tube opening with loudspeaker by
screwing in 4 self-tightening screws.
2. Activate the temperature guns. Check if air temperature of left and right side of the stack
are around equilibrium. Check the status of streaming software of the smartphone.
3. Turn on the frequency generator and ensure it is still unconnected to the thermoacoustic
unit and configure to experiment’s amplitude and frequency.
4. Open channel 1 on oscilloscope and check if the signal from the frequency generator is a
perfect sine wave.
5. Record the initial temperature. Put on the earmuff. Connect cathode and anode of the
frequency generator and the Thermoacoustic unit together. Start timer.
6. Switch the oscilloscope to channel 2 and conduct minor adjustments on the frequency
knob of the function generator. Stop when the signal from microphone reaches maximum
amplitude, indicating the reach of a resonance frequency / harmonic.
7. Exit the room and close the door; Go to another room where a laptop is livestreaming the
smartphone. Record data of the air temperatures left and right of the stack every 60
seconds for 15 minutes.
8. When experiment is finished, re-enter the test room with earmuff on and unplug the wires
connected to the thermoacoustic unit. Unscrew the loudspeaker, remove the stack by
pulling the excess fishing line, and place the structure to upright to let temperature in the
46
test tube to reach equilibrium with the air thus minimize the effect on next experiment.
Let it rest at least 5 minutes before the next run.
Appendix D - Experiment Setting Data
Loudspeaker Data
Table D.1 Loudspeaker’s current, potential difference, sound level in three settings.
Setting Current / A (± 0.001 A) Potential difference / V
(± 0.0001 V)
Sound level / dB (± 0.1 dB)
Low
Medium
High
0.000253
0.000629
0.000062
0.0270
0.0743
0.1171
102.2
108.3
111.5
Note. Measured with a multimeter connected to the loudspeaker on settings of 2000 µA and 2000 mV, and sound
level is measured by sound level sensor placed 1.0cm ± 0.05 cm in front of the loudspeaker. The current and
potential difference measurement might be inaccurate because the current is being outputted as a sine function.
Since sound intensity levels can be expressed as
𝐼(𝑑𝐵) = 10 log10(𝐼
𝐼0) 𝑑𝐵
Where I is the intensity and I0 is the constant reference sound intensity.
Thus, the increase in loudness represents an increase in sound intensity I.
Environment Data
Room Temperature Troom = 22.0 ± 0.1°C
Atmosphere Pressure P = 1 atm = 101.325 kPa
47
Appendix E - Experiment Raw Data
Stack Setting 1 Data
Table E.1 Temperature across stack when placed 4.0 ± 0.1 cm away from tube opening
under fundamental frequency with high amplitude during 900 seconds interval (1.1)
Time t / s
(± 0.1 s)
Temperature of air left to
the stack T1 / °C
(± 0.1 °C)
Temperature of air right
to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT = T2
– T1 / °C (± 0.2 °C)
0.0 22.1 24.0 1.9
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
22.1
22.1
22.1
22.1
22.2
22.3
22.2
22.3
22.4
22.5
22.6
22.7
22.9
22.9
23.0
24.3
24.3
24.7
25.3
26.2
26.8
27.4
28.7
28.7
29.1
29.7
30.7
30.9
30.8
31.0
2.2
2.2
2.6
3.2
4.0
4.5
5.2
6.4
6.3
6.6
7.1
8.0
8.0
7.9
8.0
Note. Produced with loudspeaker at high amplitude (see Table D.1) and a frequency f = 1378.8 ± 0.1 Hz.
Stack Setting 2 with High Amplitude Data
Table E.2 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with high amplitude during 900 seconds interval (1.2.1)
Time t / s
(± 0.1 s)
Temperature of air left to
the stack T1 / °C
(± 0.1 °C)
Temperature of air right
to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT = T2
– T1 / °C (± 0.2 °C)
0.0 22.3 23.1 0.8
48
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
21.9
21.9
21.9
21.9
21.9
21.9
21.9
22.0
21.9
22.0
22.1
22.1
22.1
22.1
22.3
22.9
22.9
22.9
22.8
22.8
22.8
22.8
22.8
22.9
22.9
22.9
23.0
23.1
23.1
23.2
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.8
1.0
0.9
0.8
0.9
1.0
1.0
0.9
Note. Produced with loudspeaker at high amplitude (see Table D.1) and a frequency f = 1134.3 ± 0.1 Hz.
Table E.3 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with high amplitude during 900 seconds interval (1.2.2)
Time t / s
(± 0.1 s)
Temperature of air left to
the stack T1 / °C
(± 0.1 °C)
Temperature of air right
to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT = T2
– T1 / °C (± 0.2 °C)
0.0 21.8 21.8 0.0
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
22.0
22.1
22.1
22.1
22.2
22.2
22.1
22.2
22.3
22.4
22.4
22.4
22.6
22.1
22.1
22.2
22.3
22.3
22.3
22.4
22.4
22.5
22.7
22.8
22.9
23.0
0.1
0.0
0.1
0.2
0.1
0.1
0.3
0.2
0.2
0.3
0.4
0.5
0.4
49
840.0
900.0
22.6
22.7
23.1
23.2
0.5
0.5
Note. Produced with loudspeaker at high amplitude (see Table D.1) and a frequency f = 1172.3 ± 0.1 Hz.
Table E.4 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with high amplitude during 900 seconds interval (1.2.3)
Time t / s
(± 0.1 s)
Temperature of air left to
the stack T1 / °C
(± 0.1 °C)
Temperature of air right
to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT = T2
– T1 / °C (± 0.2 °C)
0.0 24.7 25.0 0.3
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
25.1
25.1
25.2
25.3
25.3
25.3
25.3
25.3
25.4
25.4
25.4
25.4
25.5
25.5
25.6
25.3
25.4
25.4
25.4
25.4
25.6
25.6
25.6
25.7
25.8
25.9
25.9
26.0
26.1
26.2
0.2
0.3
0.2
0.1
0.1
0.3
0.3
0.3
0.3
0.4
0.5
0.5
0.5
0.6
0.6
Note. Produced with loudspeaker at high amplitude (see Table D.1) and a frequency f = 1174.0 ± 0.1 Hz.
Stack Setting 2 with Medium Amplitude Data
Table E.5 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with medium amplitude during 900 seconds interval (2.1.1)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
50
0.0 23.8 23.8 0.0
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
23.8
23.8
23.9
23.9
24.1
24.0
24.1
24.1
24.1
24.1
24.1
24.1
24.1
24.1
24.1
23.8
23.8
23.9
23.9
23.9
24.0
24.1
24.1
24.1
24.1
24.1
24.1
24.1
24.1
24.1
0.0
0.0
0.0
0.0
-0.2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Note. Produced with loudspeaker at medium amplitude (see Table D.1) and a frequency f = 1217.7± 0.1 Hz.
Table E.6 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with medium amplitude during 900 seconds interval (2.1.2)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 18.1 17.9 -0.2
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
18.3
18.3
18.3
18.4
18.4
18.5
18.6
18.6
18.7
18.8
18.1
18.2
18.3
18.4
18.4
18.5
18.6
18.8
18.9
18.9
-0.2
-0.1
0.0
0.0
0.0
0.0
0.0
0.2
0.2
0.1
51
660.0
720.0
780.0
840.0
900.0
18.8
18.9
18.9
18.9
19.1
19.1
19.2
19.3
19.4
19.5
0.3
0.3
0.4
0.5
0.4
Note. Produced with loudspeaker at medium amplitude (see Table D.1) and a frequency f = 1165.8± 0.1 Hz.
Table E.7 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with medium amplitude during 900 seconds interval (2.1.3)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 19.6 19.6 0.0
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
19.7
19.7
19.8
19.9
19.8
19.8
19.9
19.9
19.9
19.9
19.9
20.1
20.1
20.1
20.1
19.6
19.7
19.7
19.7
19.8
19.8
19.8
19.9
19.9
20.1
20.1
20.1
20.2
20.3
20.4
-0.1
0.0
-0.1
-0.2
0.0
0.0
-0.1
0.0
0.0
0.2
0.2
0.0
0.1
0.2
0.3
Note. Produced with loudspeaker at medium amplitude (see Table D.1) and a frequency f = 1163.6± 0.1 Hz.
Stack Setting 2 with Low Amplitude Data
Table E.8 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with low amplitude during 900 seconds interval (2.2.1)
52
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 20.4 20.5 0.1
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
20.6
20.7
20.8
20.9
21.0
20.9
20.9
21.0
20.9
20.9
21.0
20.9
20.9
20.9
20.9
20.7
20.8
20.9
20.9
21.0
21.0
21.1
21.1
21.1
21.0
21.0
21.0
20.9
20.9
20.9
0.1
0.1
0.1
0.0
0.0
0.1
0.2
0.1
0.2
0.1
0.0
0.1
0.0
0.0
0.0
Note. Produced with loudspeaker at low amplitude (see Table D.1) and a frequency f = 1175.9± 0.1 Hz.
Table E.9 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with low amplitude during 900 seconds interval (2.2.2)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 19.5 19.6 0.1
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
19.5
19.5
19.5
19.4
19.4
19.4
19.4
19.4
19.3
19.3
19.3
19.3
19.3
19.3
19.2
19.2
-0.2
-0.2
-0.2
-0.1
-0.1
-0.1
-0.2
-0.2
53
540.0
600.0
660.0
720.0
780.0
840.0
900.0
19.3
19.4
19.3
19.3
19.3
19.3
19.3
19.2
19.2
19.3
19.2
19.1
19.1
19.1
-0.1
-0.2
0.0
-0.1
-0.2
-0.2
-0.2
Note. Produced with loudspeaker at low amplitude (see Table D.1) and a frequency f = 1169.3± 0.1 Hz.
Table E.10 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under fundamental frequency with low amplitude during 900 seconds interval (2.2.3)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 19.3 19.3 0.0
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
19.3
19.3
19.3
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.4
19.2
19.3
19.3
19.3
19.3
19.2
19.3
19.4
19.3
19.3
19.3
19.3
19.3
19.3
19.3
-0.1
0.0
0.0
-0.1
-0.1
-0.2
-0.1
0.0
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
-0.1
Note. Produced with loudspeaker at low amplitude (see Table D.1) and a frequency f = 1168.1± 0.1 Hz.
Stack Setting 2 with High Amplitude and 2nd Harmonic Data
54
Table E.11 Temperature across stack when placed 9.0 ± 0.1 cm away from tube opening
under 2rd harmonic frequency with high amplitude during 900 seconds interval (3.1)
Time t / s
(± 0.1 s)
Temperature of air left
to the stack T1 / °C
(± 0.1 °C)
Temperature of air
right to the stack T2 / °C
(± 0.1 °C)
Temperature difference
between air to the right
and left of stack ΔT =
T2 – T1 / °C (± 0.2 °C)
0.0 19.1 19.1 0.0
60.0
120.0
180.0
240.0
300.0
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
19.1
19.2
19.2
19.2
19.1
19.2
19.2
19.2
19.2
19.3
19.3
19.4
19.4
19.5
19.5
19.1
19.1
19.3
19.3
19.3
19.4
19.4
19.5
19.6
19.7
19.8
19.9
20.1
20.2
20.3
0.0
-0.1
0.1
0.1
0.2
0.2
0.2
0.3
0.4
0.4
0.5
0.5
0.7
0.7
0.8
Note. Produced with loudspeaker at loud amplitude (see Table D.1) and a frequency f = 2295.9± 0.1 Hz.
Heating Effect of Loud Speaker Data
Table E.12 Loudspeaker temperature (inside, outside) during 900 seconds interval (4)
Time t / s
(± 0.1 s)
Surface temperature of
loudspeaker’s
diaphragm T3 / °C
(± 0.1 °C)
Surface temperature of
loudspeaker’s case on side
away from the tube T4 / °C
(± 0.1 °C)
Surface temperature
difference across
loudspeaker ΔT = T4 –
T3 / °C (± 0.2 °C)
0.0 25.1 24.8 -0.3
60.0
120.0
180.0
240.0
300.0
38.9
45.1
48.7
52.3
55.4
50.3
61.3
69.4
75.4
79.5
11.4
16.2
20.7
23.1
24.1
55
360.0
420.0
480.0
540.0
600.0
660.0
720.0
780.0
840.0
900.0
57.2
59.1
60.9
62.1
63.3
63.8
64.3
64.8
65.6
65.9
82.3
84.1
85.3
86.3
87.1
87.7
88.0
87.9
88.4
88.5
25.1
25.0
24.4
24.2
23.8
23.9
23.7
23.1
22.8
22.6
Note. Produced with loudspeaker at high amplitude (see Table D.1) and a frequency f = 1217.7 ± 0.1 Hz.