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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

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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

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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

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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

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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

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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 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 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.

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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)

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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)

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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

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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)

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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)

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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.

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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).

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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


computer animations produced by Swift and Ward (2014). 3 Screenshotted from frame 7 of the standing-wave thermoacoustic engine or refrigerator animation program in


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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



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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



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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)



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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

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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.

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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.

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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.

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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.

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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.

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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)



Experiment 2: Relationship between amplitude of speaker and temperature difference

2.1.1 Medium Fundamental Location 2 (9.0 ± 0.1 cm)



2.2.1 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

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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


under fundamental frequency with high amplitude during 900 seconds interval (1.2.1)

Time t / s

(± 0.1 s)


the stack T1 / °C

(± 0.1 °C)



(± 0.1 °C)




– 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




Time t / s

(± 0.1 s)


the stack T1 / °C

(± 0.1 °C)



(± 0.1 °C)




– 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




Time t / s

(± 0.1 s)


the stack T1 / °C

(± 0.1 °C)



(± 0.1 °C)




– 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


Stack Setting 2 with Medium Amplitude Data


under fundamental frequency with medium amplitude during 900 seconds interval (2.1.1)

Time t / s

(± 0.1 s)

Temperature of air left


(± 0.1 °C)

Temperature of air

right to the stack T2 / °C

(± 0.1 °C)



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.



Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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




Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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


Stack Setting 2 with Low Amplitude Data


under fundamental frequency with low amplitude during 900 seconds interval (2.2.1)

52

Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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.



Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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




Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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


Stack Setting 2 with High Amplitude and 2nd Harmonic Data

54


under 2rd harmonic frequency with high amplitude during 900 seconds interval (3.1)

Time t / s

(± 0.1 s)



(± 0.1 °C)

Temperature of air


(± 0.1 °C)




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


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