So No 1

Sonoluminescence: Sound Into Light

Objective: To build an experiment capable of achieving successful sonoluminescence. For this setup to be reproduced with ease. Future experiments may wish to modify and improve on the existing design and to investigate the phenomenon of sonoluminescence in greater detail. A section with some suggestions has been included in this manual.

Introduction

The History: Sonoluminescence (SL) was discovered accidentally in 1934 by two German scientists at the University of Cologne as a result on their experiments with sonar. They placed an ultrasonic transducer into a drum filled with photo developing fluid in hopes of speeding up the developing process. The fluid was full of thousands of tiny, short-lived bubbles. Once the pictures were developed, they noticed small dots on the pictures. They realized that the bubbles in the fluid were emitting light when the acoustic field from the transducer was turned on. Due to the complexity of their setup, the effect was not properly investigated. In 1989, Felip Caitan and Lawrence Crum produced the first single bubble SL. Single bubble SL, the kind used in this laboratory experiment, traps a single bubble at the anti-node of a standing acoustic wave. The bubble emits light during each compression of the wave, hence twice per period. Within the controlled environment of a single bubble, many facts about SL have been uncovered [1].

The Process: Sonoluminescence is the conversion of sound energy into light energy. Sound waves are aimed at an air bubble trapped in a flask. The sound waves cause the bubble to oscillate furiously: (a) the bubble starts out at a size around 5 microns (millionths of a meter); (b) then it expands to a maximum size (not to scale) of about 50 microns. At this large size there is a near-vacuum inside the bubble because of the relatively few air molecules present. This low-pressure near-vacuum region is surrounded outside the bubble by a much higher-pressure region, which causes (c) a catastrophic collapse of the bubble to between 0.1 and 1 microns. During this compression phase a flash of light (d) emerges from the bubble [2]. The conversion of low energy density sound waves into light requires a concentration of energy by a factor of 1 trillion!!

The Theory: Various theories exist as to what causes the bubble to emit light. The most outrageous was suggested by Claudia Eberlien: that emitted light is a form of Hawking radiation. Stephen Hawking postulated that when virtual photons are created in the vacuum near the event horizon of a black hole, some fall into the black hole and some escape, causing the black hole to radiate. In the context of SL, the basic idea is that as the bubble expands, a near-vacuum is formed. The virtual

photons experience extreme changes during the collapse process, and some are converted into real photons [3]. Under this theory, the light emitted should only depend on the vacuum interface movement. The experimental fact that bubbles dropped with inert gases change the characteristics of emitted light is strong evidence against this theory. Andrea Prosperetti believes that the light is generated as a jet of liquid shoots from one side of the bubble to the other at very high speed (around 6000 kilometers per hour). Wint-O-Green Lifesavers can give off light when they crack, a process known as triboluminescence. It is thought that the high pressures inside the bubble cause the water to form ice-like structures. As the jet hits the other side the water "fractures" in the same way non-Newtonian fluids behave like solids when subjected to sudden stresses. The fracture causes a release of photons. Prosperetti believes that an introduction of noble gases changes the way the water molecules align themselves creating flaws in the crystal-like structure that enhance the fracturing effect. This theory may be tested by firing hyper-fast jets of water to see if it produces light without the acoustic cavitation. [3] Recent experiments with high speed cameras show no wet jets [1]. Prosperetti himself has renounced this theory. Dr. Putterman of UCLA introduced a more widely accepted theory known as shock wave SL. Shock wave theory suggests that as the bubble collapses, it retains its spherical shape, thus creating a high pressure system within the bubble. As the bubble nears its minimum radius, the Van Der Waals force become significantly large and almost instantly stops the bubble from collapsing any further. This fast deceleration of the bubble walls can exceed 107 times that of gravity. Even though the walls have stopped, a shock wave continues to travel towards the center of the bubble. The energy contained in the shock wave then becomes focused at the centralized point of the bubble and creates an area of extremely high temperatures. These temperatures result in the production of plasma and begin to emit photons in a process known as thermal Bremsstrahlung. The photons emitted from this process is over a broad spectrum [4][5][6]. Putterman is recognized as the SL expert. He has written many popular articles in Scientific American, Nature, and Physics World.

The Facts: Photons are emitted from the bubble into a continuous spectrum, suggesting blackbody radiation. Using the Wien's displacement law, the peak intensity of the emitted spectrum has been estimated at temperatures exceeding 10,000 degrees Celsius, possibly being as high as 1,000,000 degrees Celsius based on some models. Some other interesting facts about sonoluminescence [1]: •

The light flashes from the bubbles are extremely short—between 35 and a few hundred picoseconds long.

•

The bubbles are very small when they emit the light—about 1 micrometer in diameter.

•

Single-bubble sonoluminescence pulses can have very stable periods and positions. In fact, the frequency of light flashes can be more stable than the rated frequency stability of the oscillator making the sound waves driving them.

•

For unknown reasons, the addition of a small amount of noble gas (such as helium, argon, or xenon) to the gas in the bubble increases the intensity of the emitted light dramatically.

•

The application of a magnetic field will increase the intensity of the emitted light [7]

•

Water temperature affects the intensity of emitted light, with a maximum at 13 degrees Celsius [8]. At higher temperatures thermal motion will disrupt the spherical shape of the bubble, while at lower temperatures the drop may be due to the onset of ice nucleation.

Scientists at the University of Illinois, lead by Dr. Kenneth Suslick, have recently proved the existence of plasma within an SL-ing bubble. Plasma consists of ionized gas or simply a system of charged particle. This state of matter only exists at high temperatures. Unfortunately, this gives no indication of the actual temperature within the bubble, but shows enough evidence to support the idea of very high temperatures being reached during this process and the possibility for fusion. The figure below is a picture of plasma produced in a

sonoluminescence process.

Sonoluminescence in Nature: Recently, Pistol Shrimp were found to produced SL as a byproduct of their specialized claw closing quickly [9].

Sonoluminescence as a basis for fusion: In the past 4 years there have been two reported successes at achieving “bubble fusion,” a term coined for fusion taking place inside of a collapsing SL bubble. R. P. Taleyarkhan;s lab group, using deuterated acetone, show measurements of tritium and neutron output consistent with fusion, but these measurements have not been reproduced outside of the Taleyarkhan lab and remain controversial. Writing in Nature, chemists David J. Flannigan and Kenneth S. Suslick study argon bubbles in sulfuric acid and show that ionized oxygen, sulfur monoxide, and atomic argon populating high-energy excited states are present implying that the bubble has a hot plasma core. They point out that the ionization and excitation energy of dioxygenyl cation is 18 electron volts, and thus cannot be formed thermally; they suggested it was produced by high-energy electron impact from the hot opaque plasma at the center of the bubble [10] [1]. Flannigan's results corroborate the fusion claim made by Taleyarkhan. Putterman has also recently claimed to have achieved fusion in his laboratory[11] A recent business venture, Impulse Devices, has been created to develop bubble fusion technology (http://www.impulsedevices.com).

Lab Equipment and Materials

Lab Equipment

1) Oscilloscope with 2 input channels. A digital oscilloscope which can be connected to a computer would be useful for examining certain properties of the bubble, but is not necessary 2) Sine function generator which can be set to within +-25 Hz of flask resonance (flask resonance should be within 25-35 KHz). Due to the necessary precision, it is highly recommended that a digital generator is used as Sonoluminescence will only occur exactly at resonance. We used a BK precision 5 MHz, +- .9%. 3) Soldering equipment. It should be noted that the piezos have a Currie temperature (above which they begin to loss their dipole moment) around 450 Celsius. This happens to be the melting point of most solder. Please follow soldering instructions carefully, and if available, use a solder gun with temperature control. 4) Bunsen Burner and ring stand with wire mesh. This will be used to degas the water. There are many different ways to degas water, if you decide to use a different technique you do not need these items. 5) Inductors. The exact value of the inductor will depend on your flask resonance and effective capacitance. Typical values will be between 15 – 30 mH. We used variable inductors which are located in the advanced lab. Inductors add in series, so one can obtain greater inductance by attaching one or more together. It maybe necessary (if the required inductance is too high or low, or if the current exceeds the range specified for safe operation of the inductors) to build an inductor from coil and an iron rod. 6) Amplifier. It was found that sonoluminescence will occur with very little wattage. It maybe that the signal generator can deliver enough power to the circuit for sonoluminescence (which is the case for ). However, it might either be necessary or interesting to experiment with higher wattages.

CAUTION: read carefully at the end of this lab (under supplemental materials) the proper way to wire an amplifier. Because of the high wattage it will be necessary to obtain a DC power source capable of delivering large amperage. CAUTION: The variable inductors presently used in this lab are rated for use in the milliamp range. It will be necessary to build an inductor from coil and iron which is capable of handling high currents. 7) (OPTIONAL) Multi-meter with ability to read capacitance and inductance. It may either be interesting or necessary to know the capacitance or inductance of the circuit. The piezos used from channel industries have capacitance listed at the end of this manual. For diagnostic purposes one might also need to measure voltage or current.

Materials (flask or piezo dimensions could be varied in future experiments) *2 - Large piezoelectric transducers (driving units): 20mm diameter by 4.4mm thick with an 8mm diameter hole through the center *1 - Small piezoelectric transducer (microphone): 6mm diameter by 2mm thick 1 – Tube of two-part epoxy 1 – 100 ml spherical flask 2 – 175 ml Erlenmeyer flasks 2 – Rubber Stoppers 1 – Ring Stand 1 – Three finger clamp 1 – Small diameter syringe and needle Several of the following: Coaxial cable BNC plugs 36 AMG wire

*A sonoluminescence PZT kit containing 2 large and 1 small may be purchased directly from:

CHANNEL INDUSTRIES, INC. 839 Ward Drive Santa Barbara, CA 93111 (805) 967-0171 [email protected]

Creating Sonoluminescence: An Introduction

Signal Generator and Amplification: Creating sonoluminescence can be done with the standard laboratory equipment listed above. A signal generator is needed to supply the correct frequency for the apparatus and can act as a source of power. Initially it was thought that an audio power amplifier was needed to boost the signal from the signal generator, however we found that the output from the signal generator alone was sufficient drive to create SL. Should an amplifier be desired in the future, the lab has acquired a standard audio amp of 300W (see appendix F for amplifier specs). The amplifier does have its drawbacks. For one, its specified range of operation is up to about 25 kHz, which may be below the frequency necessary for SL. It will be necessary to test the amplification gain (Vout /Vin ) as a function of frequency (see appendix D). This will be difficult to test as most voltmeters cannot operate at such high frequencies and the

oscilloscope's resistance is too high. Furthermore, it's current output is too great to use the lab's variable inductors. The resonant frequency we found for our flask caused us to abandon the amplifier as the frequency was outside the range of the amplifier's specifications and we did not have time to test the gain. Piezo-Ceramic Transducers: The heart and soul of the SL circuit are the two Piezo-Ceramic Transducers. The piezoelectric are the driving elements of the system, producing the sound for SL. The Piezo is made up of a special type of ceramic with a “built in” dipole momet. When a voltage is applied to it, will expand or contract depending on the direction of current. By applying AC voltage across the piezo, a sound wave will be produced at the frequency output from the signal generator. If you ordered the transducers from Channel Industries they will be resistant to water. The piezo's ceramic has a permanent polarization, which is created by heating the piezo's above their "Curie Point," around 450C, and then cooled. This polarization will remain unless the piezo is heated above it's Curie Point. This will become important when soldering on the leads. The polarization defines positive and negative as marked on the piezo's with red X’s. More information about the piezo's from Channel Industries, such as their capacitance, can be found in the appendix E. Flask: The next element is the 100ml spherical bottomed flask. We wish to create a three-dimensional standing acoustic wave inside the flask, which will be able to trap and SL a single bubble. According to many internet websites, a spherical flask is necessary for SL. Inductor: The inductor is needed to resonate the circuit, thereby delivering maximum power to the flask. Inductance is measured in Henries (Webbers/second). Typical values for SL will be around 20 mH. Because we will not know correct resonant frequency of the flask beforehand and because this frequency can change, a variable inductor is essential. If you plan on using a low current source, such

as the signal generator, it will be easier to use the variable inductors located in the lab. There are three, each going up to about 25 mH. By attaching all three together we can achieve 75 mH. However, if higher currents will be used, or if the necessary inductance is greater than 75 mH, you will have to build one (they are hard to buy). This is easy, using a coil and iron rod. The wire needs to be thick enough to handle your current. Calculate the inductance with the following:

If you are using an iron rod, multiply this by the relative permeability of iron, which is about 200. This number can also be measured using some voltmeters. If one is not available, connect the inductor in an RL circuit and attach to a DC power supply. Measure the voltage across the inductor on the oscilloscope. When you switch on the power, your trace should look like the following:

Use the equation VL = L*(dI/dt) = -V0*e^(-Rt/L) to figure out the inductance. This can be done by noting the time scale of your oscilloscope, and finding where the voltage is roughly 1/e the initial voltage. We then have t=L/R. You can figure out the net resistance by setting a voltmeter to read ohms, and putting it across the RL circuit.

Apparatus Setup

First, solder 36 AWG wire onto each side of the piezos. Cut the wire into about 10 cm pieces. It is recommended that on whichever side will be facing the flask, solder 3 equidistant wire leads. This will help balance the piezo, and the other two can serve as backups in case one of them breaks off. Soldering will take place around the Currie point, so make sure to work quickly. Strip the wire of its insulation and “tin” the ends for soldering. Using a clean eraser, gently rub both sides of each piezo to improve the conduction. The large piezo’s must be mounted 180 degrees apart as near to the equator of the spherical flask as possible using quick dry epoxy. They should also remain in phase, meaning, you should have either both red X sides pointing inward, towards the flask, or outward. The small piezo should be fixed directly to the bottom of the flask. With the positions of your piezo's marked, epoxy glue them to the flask and let it sit over night. To reduce the mechanical stress on the solder joints, coil the wire around a pen or pencil. Here is a picture of mounted piezo's with soldered wire leads:

Using regular copper wire around the lab, connect the large piezo’s in parallel with each other. Next connect the piezo's to the signal generator. It doesn't matter if you connect to the positive or negative, as long as both positive outputs from the signal generator go to the same side of each piezo (remember that the piezo has a polarization, giving it two distinct sides). Similarly, connect the microphone to the oscilloscope. You are now ready to resonate the flask. The only thing missing in our circuit is the inductor, but we only wish to add this after resonating the flask. Skip to the next section and return here after finding the flask resonances. (Note: many online schematics have small resistors in their circuit. This is useful for diagnostic purposes such as knowing the voltage. You may wish to do this depending on your experiment's goals) CAUTION: these wires will have very high voltages going through them. The 10 AWG wire going to the large piezo's may have upwards of 700 peak to peak volts. Either cover them with a sleeve, or use extra caution when operating the experiment. If during the experiment two bare wires touch, turn off the signal generator before touching the wires. Do not attempt to move the wires with the signal generator on. Now with the flask resonant frequencies found, we add the inductor to our circuit. Find the positive line from the signal generator (with a voltmeter). Insert the inductor between the positive

terminal and the flask. Use whatever wire or method of connection you desire. If you have built an inductor, keep the inductor at least 1 meter way from the other equipment, as the magnetic field could interfere with the equipment. Below are schematics of what the circuit should look like. ignore the 1 ohm resistor. Also, it was found that connections between the outer part of the coaxial cables were not necessary. Visit the website address in the appendix A for a video of our setup.

The Flask and Finding Flask Resonance

The flask should be nearly spherical. This is an important quality, as resonance is a geometric property of the flask. A resonant frequency occurs when there is a 3 dimensional standing pressure wave inside your flask (the bubbles will get trapped at a pressure anti-node). Before measuring the flask's resonance, go to appendix B and try calculating the expected values for an ideal situation. You should find resonance at frequencies far from these values which correspond to excited harmonic states. To find your flaks' resonance, fill the flask with ordinary tap water and connect the leads from the microphone to the oscilloscope. Fill the flask up just a little into the neck so that the water “fills out” the spherical shape of the flask. Filling it too high or low may change the resonance frequency. Note that the temperature of the water will affect the resonance frequencies. Make sure to find resonances at the temperature of operation. Therefore, it may be a good idea to allow the water to come into thermal equilibrium with the environment. Try connecting the output from the signal generator to the oscilloscope on a second channel (see picture). To do this it will be necessary to attach a BNC plug with two outputs to the signal generator.

The inductor should not be connected at this point, since we are only interested in resonant property of the flask (we will deal with the circuit's resonance later). Turn on the signal generator and oscilloscope. Configure the oscilloscope so that the signals from the microphone and generator are

easily seen on the same screen. Starting from about 17 KHz, slowly increase the frequency until the microphone signal's amplitude increases to a local maximum. Continue as high as desired, but 60 kHz should be sufficient. We found resonances around 25 kHz, 31 kHz, and 52 kHz (to mention a few). To confirm resonance, try gently squeezing the flask. This will dampen the standing wave and produce a noticeable decrease of the microphone signal's amplitude. Not all of these resonances are good for achieving SL. This can only be tested by carrying out the experiment to its end, which can be timely if your resonance or current source is such that the variable inductors cannot be used. More on this later.

Impedance Matching: Resonating the Circuit

We wish to deliver maximum power to the flask at the resonant frequencies. The piezo in our circuit acts like as a capacitor (see appendix E for the piezo's impedance of the channel industry capacitors). In an AC circuit, a capacitor that will take power away from the system. Therefore an inductor must be inserted to cancel out this impedance. This condition is known as resonating the RLC circuit. The inductance needed for the circuit can be calculated, knowing the resonant frequency and the capacitance of the piezo's (for a derivation see appendix B): f Circuit =

1 2! LC

This equation is meant only as a starting point. The true inductance will be found by connecting the inductor and observing resonance and may differ from the calculated value. For this reason, it is strongly recommended that a variable resistor is used which can cover a larger range of inductance. Even if you decide to build your own inductor, it may be helpful to use the three variable inductors in the lab for finding an exact value of inductance required, which when connected in series

will cover a range of about 0 – 70 mH. This should should be sufficient for all frequencies and capacitances. CAUTION: If you are using an inductor built with a coil an iron, beware of large fringe field effects. You should place the inductor a few meters from the setup. CAUTION: If you are using the variable inductors, they cannot be used at high currents (see label). To avoid exceeding these currents, consider placing an ammeter in series. With the inductor in place (read about this in setup), we look to resonate the circuit. Connect the microphone output to the oscilloscope. Slowly vary the inductor and watch the screen. As the inductor approaches the necessary impedance, the output from the microphone will increase in amplitude. Keep increasing the inductance until the amplitude begins to decrease, therefore finding the maximum. Make a note of the values at which your flask resonates and the corresponding number of Henries the inductor must be set at to achieve circuit resonance. How does this compare to the inductance you predicted? The peak to peak voltage maximum of the microphone will experience a dramatic increase as the circuit approaches resonance. Our microphone signal varied from a few millivolts off resonance to 5 or 6 volts at resonance. The signal should be at least a 2 or 3 volts to obtain sonoluminescence (according to some websites).

Bubble Trapping

With the circuit built it is now time to trap a bubble. Trapping a bubble can be a frustrating and laborious task until you get good at it. No SL will occur until you can successfully trap a bubble with ease. Before preparing your water for SL, try perfecting the art of bubble trapping. You should have

recorded the values for your flasks resonance and the corresponding inductance where the circuit resonates. Repeat the procedure outlined below for each resonance. Observe and record what you see for each frequency. Using the signal generator, set the frequency at resonance. Then hook-up the inductor and tune it to a maximum. The peak to peak voltage should be at least an order of magnitude larger after including the inductor. The signal generator will tend to stray from the desired frequency if you just turned it on. Let it warm up for 5 or 10 minutes for best results. It is always good to keep an eye on the microphone output. If the signal starts to weaken: re-tune. We used two different approaches for injecting a bubble, but surely there are others. Both of them start by drawing some water from the flask into the syringe. The quickest way to deliver a bubble is to hold the syringe over the surface of the water and squirt in a little water. This method will create many bubbles inside the water, and consequently pollute the water with air (which is OK for now, until you get better at the second approach). For a more effective approach, hold the tip of the syringe a few inches from the surface and squeeze a single droplet of water onto the surface. The bubbles created by the droplet’s impact on the surface will enter the water and depending on the shape of your standing wave, may move in different directions or converge on a single spot. This can be seen with the naked eye, however once a single bubble reaches a pressure anti-node, it may be too small to see. If after the droplets hit the surface the bubbles float to the top without any directed movement, the power is either too low or the system has drifted from resonance. The standing waves set-up by each frequency might be drastically different. Careful observation of how and where bubbles are trapped will help you determine which frequency is best for SL. SL was observed to occur when a very, very small bubble is trapped in nearly the middle of the flask. The bubble is so small that it maybe mistaken for a particle of dust. Try dimming the lights, using a magnifying glass, or some kind of ambient back-lighting. We observed that at a SL frequency, when a bubble was injected into the water, many tiny air bubbles in the water were immediately sucked

towards the middle. At wrong SL frequencies, trapped bubbles were usually very big (easily seen by eye) or trapped far from the middle of the flask. When a bubble is trapped it is expanding and collapsing. This will slightly interfere with the waves within the flask. Small ripples from this effect can be easily seen on the oscilloscope, the signal should appear similar to the figure below. By visiting the web address listed in the appendix A, you can see a video of how this should appear as a bubble is trapped and then dissolves.

Water Preparation

It is recommend that distilled water is used, although SL was achieved using regular tap water. Observations indicate that SL is more stable when using distilled water. Distilled water can be purchased at the chem store or a local supermarket. The water must now be degassed. Excess gas will greatly disrupt the bubble stability. Bubbles

formed within water with too much gas will grow in size and not sonoluminesce. Various methods for degassing water can be successful. Two of the most popular are boiling and vacuum pumping. Boiling is by far the easiest, and is described below. With your Bunsen burner and ring stand with wire mesh setup, place one of the Erlenmeyer flasks on top of the wire mesh. Make sure to boil enough water to fill your flask (a lot of water will be lost through boiling). If you are using the 100 ml spherical flask, boil two equal quantities of water (around 100ml apiece) in two Erlenmeyer flasks. They should be boiled for about 10 minutes apiece and then plugged with a stopper then rapidly cooled under cold water. Rapid cooling produces a vacuum in the space above the water, thereby removing more gas from the water and allowing the water to remain degassed for several days inside of these flasks.

Making the Bubble Glow With all the above steps completed, we are ready to sonoluminescence our bubble. First, make sure that the flask is clean. Ordinary hand soap should be fine, but make sure that all dust particles and soap are removed from the flask before proceeding. Do not worry about getting the piezos wet. They are made from a ceramic material and are water resistant. When filling the flask with prepared water, be careful not to pour too fast. This will introduce gas into the water and possibly prevent the bubble from SL-ing. It helps to tilt the flask at an angle, and slowly pour the water along the side. After a day or two, the water should be dumped and the flask washed out. Turn on the signal generator and connect both the generator and microphone outputs to the oscilloscope. The microphone output should be a clean sine wave. If your signal generator has a built

in amplifier, or if you are using an amplifier, you may have to adjust the input signal for SL to occur. We found that our signal was about 5 Volts peak-to-peak and the microphone output was between 2.5 and 4 volts peak to peak on the oscilloscope when SL occurred. See more on this in the section “Debugging your Bubble” below. Now try injecting a bubble with your preferred technique. To see the light, make sure to darken the lighting. The light from the bubble will be very faint and bluish (see figure 3). It may take a few minutes for your eyes to adjust to the darkness when first looking for it. Try using a magnifying glass to better see the bubble. It is advisable to keep the oscilloscope running throughout the experiment. Remain watchful of the oscilloscope. If the microphone signal starts dropping, re-tune the signal generator and inductor. Usually you do not need to disconnect the inductor to do this, just a slight adjustment of the generator frequency or inductor will be sufficient. Also, if your eyes are straining while looking for the bubble, the oscilloscope can tell you when the bubble should be glowing. The oscilloscope should look like figure 2 when sonoluminescence has been achieved (visit the website video in the appendix A). If the ripples from the microphone signal disappear, the bubble has been lost. The frequency we found to produce SL was in the 31.18-31.39 kHz range. The others trapped a bubble at the anti-nodes of the standing wave in the flask but no sonoluminescence was observed. Other 100 mL SL experiments found 25 kHz to work best. This would require more than one variable inductor, which another group was using. It might be good to check this resonance. The 52 kHz resonance trapped a large bubble near the top of the flask, and it was thought that this resonance from an excited harmonic state.

Debugging Your Bubble

It will be noted again that SL is sensitive to numerous factors. If you are having a problem SLing make sure to consider the following: -Frequency of operation: maybe this frequency is not suitable for SL. If the bubble trapping behavior (see “Bubble Trapping”) at this frequency does not match the stereotypical SL trapping behavior, try another frequency. -Stability of the signal: If the microphone output is off peak or (if you have a digital signal generator) the frequency from the signal generator is erratic, let the generator warm-up longer and try again. -Cleanliness of flask: If dust particles are floating around, try washing the flask better. -Gas content of water: If there are bubbles forming along the side of the flask, or if the bubble is magically growing in size you could try to degas the water again. -Shape of flask: If the flask is some none-spherical geometry, your standing waves will be different from the ones covered in this paper. Try consulting outside sources.

-Perfectly resonating circuit: If the you made an inductor, or the lab inductors are not in the necessary range to fully resonate the circuit, you could try using a different frequency or increasing inductance. -Water level: It was noticed that flask resonances and the maximum achievable microphone output depended heavily on how high the flask was filled with water. For example, with the water below the flask's neck, the microphone output was around .5 volts, compared to just above the flask's neck when it was between 3 and 4 volts. We observed that SL worked best when the water was filled just a little into the neck of the flask. We believe that at this level the water “fills out” the spherical shape of the flask. -Clamp treasure: The tighter the clamp is holding the flask, the greater the dampening effects will be. Try loosening the clamp for an increase in microphone signal. -Temperature changes of the water: If you are preforming the experiment after cooling, the water will not yet be in equilibrium with the environment. It is known that as the temperature increase, so does the frequency for SL. Therefore in order to maintain SL, it may be necessary to increase the frequency produced by the function generator by a few hertz every couple of minutes.

A topic not covered in the above sections because we found it to play no role in our experiment, but is mentioned in numerous websites, is the bubble's dependence on the microphone output. The microphone output can be thought of as an indicator of the energy available for SL. We found that SL occurred for peak to peak voltages in the range of 2.5 to 4 volts. These voltages may depend on such factors of flask size, bubble size, and gas content. As a guide, here is a chart of gas content vs. peak to peak signal level [12]

Suggestions for SL in the Future Hopefully we have given a solid qualitative overview of the physical process and experimental procedure necessary to duplicate this experiment. The next step should be making improvements on our design and adding instrumentation for making quantitative measurements of such quantities as bubble size, water temperature, spectra of light, intensity of light (see figure).

There are many good websites for available for achieving this. From here there are an endless number of parameters to explore. Here we discuss several things that we would like to have tried, or that would have made the experiment better. First off, it would be nice to design a system to easily disconnect the flask from the circuit for cleaning. Several times when disconnecting the wires for cleaning we had occurrences of the solder falling off. The system could either include removable piezos or perhaps a circuit board for the wires to plug into. Consider doping of the bubble with noble gas. When we reached this point, we were nearly out of time in the semester and had little chance to do a detailed investigation. To insure that the noble gas is inside the bubble, try filling the flask entirely up with water. Place the orange rubber cover over it. As you remove some water from the flask with the syringe, inject in gas. Try exposing the flask to a magnetic field and note the effects on the light produced. Other variables such as water temperature, different liquids, flask dimensions could all be varied. If you have access to a digital oscilloscope, it could be possible to analyze the bubble's motion by recording the microphone signal and subtracting off the signal with no bubble present.

Appendix A For SL videos go to the following website: You can access videos for:

Appendix B Derivation of Acoustical Resonance Inside the Flask[13]

The harmonics inside the flask can be solved for assuming the perfectly spherical flask, that the

pressure waves obey the wave equation, and the appropriate boundary conditions. Let P(r,t) be the pressure, 'v' the velocity of sound in water, and 'a' the radius of flask. We have:

Assuming finite pressure at the origin, we know the solution of this equation to be:

where k is the wave number (k=!/v), ! is the angular frequency, J is the spherical Bessel function, and P is the associative Legendre polynomials. We assume the harmonics exhibit spherical symmetry by taking l=m=0, and assume that the pressure at the r=a is zero (this is a good approximation since the acoustic impedance of water is much higher than that of air). Looking at the none-excited solutions to this equation, resonance occurs at the zero's of the Bessel function (none-excited => Legendre polynomial = 1). These zeros are give in general by:

and the resonance frequencies for an Lth order is:

With l = 0 we have a relation for resonance:

Knowing the speed of sound in water is 1435 m/s, we can calculate all the resonance frequencies for none-excited by measuring the flasks radius. The Best way to do is is finding the circumference and dividing by 2".

Appendix C Derivation of Impedance Matching condition

In a simple RLC circuit shown below (our circuit can be reduced to this diagram):

We define the total impedance of the circuit as Z = R +XL + XC where XL XC can be found to equal:

These values follow from solving Kirchoff's law applied to an LC circuit:

In AC circuitry, L and C impedance are complex quantities, hence to find Z's magnitude we use the Pythagorean theorem:

Using V=IR we have:

Power I2R. Therefore power is inversely proportional to

For a fixed R, power is therefore maximum when L and C impedances are equal. This condition leads to :

Appendix D Amplifier Diagnostics

Amplification is an increase in voltage amplitude of a waveform, and is measured with gain=Vout/Vin. Amplifiers are rated to operate within a range of upper and lower frequencies. Gain decreases as the signal moves further out of the range. An ideal amplifier's gain will look like something like the below plot. For our ideal amplifier, the range of operation would be between w1 and w2.

If you are planning to operate the an amplifier out of range, test the gain at points between w1 and w2, and then out near the frequency of operation. A significant drop in gain means the amplifier should not be used.

Appendix E Piezoelectric Transducer Stat Sheet

Appendix F Audio-amplifier Stat Sheet

Works Cited

[1] http://en.wikipedia.org/wiki/Sonoluminescence

[2] http://www.aip.org/png/html/sono1.htm [3] http://www.freeglossary.com/Sonoluminescence [4]Putterman,Seth(1998) Sonoluminescene: the Star in a Jar, Physics World, May, 38-42. [5]Putterman,Seth.(1995) Sonoluminescence, Sound into Light., Scientific American, Feb., 33-37. [6] http://personnel.physics.ucla.edu/directory/faculty/index.php?f_name=putterman [7] http://prola.aps.org/abstract/PRE/v60/i2/p1759_1 (real 9...push others up) [8] http://www.iop.org/EJ/abstract/0022-3727/1/5/415 (real 10) [9] http://www.nature.com/cgitaf/DynaPage.taf?file=/nature/journal/v413/n6855/abs/413477a0_fs.html [10] http://www.nature.com/nature/journal/v434/n7029/abs/nature03361.html [11] http://pesn.com/2005/04/28/6900088_UCLA_Cold_Fusion/ [12] http://www.techmind.org/sl/ [13] http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ54377.pdf