Observation and Characterization of Sonoluminescence

Sonoluminescence’ describes the production of light during rapid collapse and expansion of bubbles that have been placed at the anti-nodes of a standing ultrasonic sound wave. Although the physical mechanism through which this light is produced has not yet been confirmed, there are a few prominent theories. In this experiment, sonoluminescence in the Teachspin apparatus has been obtained and photographed. Light pulse characterization was attempted, but no experimental rise times have been obtained. A quality factor the for resonance in our system has been obtained.

Introduction

The phenomenon of sonoluminescence was first observed in 1934 by H. Frenzel and H. Schultes at the University of Cologne. They were conducting research on marine acoustic radar which involved strong ultrasonic fields, when they observed chaotic clouds of light-emitting bubbles. These clouds have come to be known as “multi-bubble sonoluminescence.” These bubbles were not closely studied until 1988 when D. Felipe Gaitan was successfully able to isolate a single sonoluminescing bubble in a spherical flask. Modern physical explanations for sonoluminescence range from plasmas, to ionisation and photo-recombination, Bremsstrahlung radiation, fusion, and even processes similar to Hawking radiation.

Light pulse durations that are emitted from these isolated bubbles has been determined experimentally to be shorter than 100 picoseconds in duration, and are incredibly regular in frequency. It has also been observed that the light intensity of the bubbles is highly dependent upon the temperature of the water in which they are contained, with brighter light being produced by water that is close to freezing. Additionally, degassing the water with a vacuum pump is necessary for the bubbles to remain stable at resonance.

The Teachspin setup that has been used in this experiment employs a plastic square prism containing water as the sonoluminescence cell. A high frequency sound generator is placed at the top of the water, and a standing wave is formed during resonance by adjusting the sound frequency. A small metal boiler is used to seed bubbles which are subsequently trapped at the anti-nodes of the standing wave by convergent pressures. By increasing the sound amplitude, the bubbles will begin to sonoluminesce. If the sound amplitude is increased past this point, the bubbles will dissolve immediately. By carefully controlling the conditions in the cell, sonoluminescence may be observed and reproduced using the Teachspin apparatus.

Resonant frequencies for a rectangular prism are given by

$f=\frac{v}{2\pi}\left[ \left(\frac{n_x \pi}{L_x}\right)^2+\left(\frac{n_y \pi}{L_y}\right)^2+\left(\frac{n_z \pi}{L_z}\right)^2\right]^{1/2}$

Where $L_i$ is the length of the prism along a direction, and $n_i$ is the number of antinode s in that direction. For a certain set of dimensions, the resonant frequency can be indexed by the mode notation $[n_x,n_y,n_z]$.

With our cell, we need two vertical antinodes that can be used to trap bubbles. The source of sound will also be at an antinode, so we will be using the [1,1,3] resonant mode, which is shown in the figure below.

To calculate the quality factor ($Q$) of our resonance, we can measure the full width half-max of frequency with respect to transducer voltage ($\Delta f$).

$Q= \frac{f_{\text{res}}}{\Delta f}$

This factor describes the sharpness’ of a resnonace peak, and is related to how damped the system is.

Materials:

Teachspin SL100B Sonoluminescence Control Box
Teachspin Cell and Transducer Unit
Teachspin Ultrasonic Horn
Hydrophone
Ramsey SG-550 HF Audio Function Generator
TektronixTDS 2024 Digital Oscillioscope
3mH Inductor
Water Boiler Connection Cable
Photomultiplier Tube
2000mL Vacuum Flask and Vacuum Pump
Ring Stands
Deionized Water
Digital Camera (Optional)

After laying out the equipment, the first step was to make the necessary connections. Power was given to the control box, function generator, and oscilloscope directly using their respective power supplies.. The control box then provides the necssary power to the boiler, PMT, and transducer box in course of the experiment. The basic connections are shown below.

To prepare the water, approximately 500 mL of deionized water was placed in a vacuum flask. The water was then pumped on with a vacuum pump for approximately two hours. Following this the water was placed in a refrigerator for 30 minutes, and then was pumped on for another 10 minutes. By the time the experiment began, the water was usually about 10 °C. The water was also used at room temperature once to observe the impact of temperature on light intensity.

The square prism cell was filled to a height of 10.0 $\pm$ 0.1 cm, and the ultrasonic horn was submerged to a depth of 1.0 $latex\pm$ 0.1 cm. To find resonance, a frequency of 25 kHz was selected on the function generator, and the frequency was increased until the peak voltage of the sinusoidal transducer signal reached a maximum. The observed resonant frequency varied significantly between different runs, and drifted as the water warmed up during the experiment.

$\rightarrow$ Generally, resonance was observed between 26.3 kHz and 27.0 kHz.

After finding resonance, the peak transducer voltage was set to 500 mV, and the transducer voltage was measured for driving frequencies in intervals of 10 Hz near resonance. These were measured so that a quality factor for the system could be obtained.

To probe the pressure amplitude at various points in the cell, the hydrophone was used. The hydrophone consists of a short metal rod with a pressure sensitive tip. By placing the tip of the hydrophone in the desired measurement location, a proportional voltage can be viewed on the oscilliscope. The hydrophone was used to qualitatively characterize the acoustic pressure along an the axis directly below the ultrasonic horn.

Obtaining Sonoluminescence:

Using a fresh batch of water, resonance was obtained. Following this, the boiler coil was placed toward the bottom of container. After inserting the coil, resonance was restored. Peak transducer voltage was increased to 600 mV, and the boiler button on the control box was pressed for a brief pulse of less than one second. Depending on the placement of the coil, bubbles would be drawn into the antinodes of the standing wave. If the cell was at resonance, these bubbles would initially vibrate and then collapse into a very tiny, but visible, stable speck.

If the transducer voltage was lower, say 200 mV, the bubbles would slowly drift toward the nodes rather than be ‘sucked in’. If the transducer voltage was less than about 100 mV, the bubbles would simply float to the surface. If the coil was not well positioned for seeding both antinodes, a technique to seed both was to keep the voltage very low, and as a bubble was floating past the upper antinode increasing the voltage to draw it in. The boiler could be used a second time to seed the lower antinode.

After ‘catching’ bubbles in the antinodes, the sound amplitude was increased slowly until sonoluminescence was observed. The phenomenon is very difficult to see unless you are in complete darkness, and your eyes have had time to become well adjusted. It is much easier to see the characteristic high frequency signal on the oscilloscope, which is shown below. Sonoluminescence was observed at a peak transducer voltage of approximately 2.2 V.

Oscilloscope display of transducer voltage output during sonoluminescence. The top signal has a high frequency filter, and the bottom signal is the unfiltered voltage output which shows the sinusoid of the driving frequency.

To photograph this phenomenon, a high resolution digital camera was used. The exposure time was set for 30 seconds following a 2 second delay. Macro and 55 mm camera lenses were used.

Troubleshooting (Problems that were encountered during this experiment):

– Make sure that transducer voltage is being read by the oscilloscope at a 1x gain.
– If the horn makes a screeching sound, and the hf filtered transducer signal is covered with noise, immediately reduce the horn amplitude. This is caused by tiny bubbles that can cause pits on the end of the horn. If this happens, it is possible that the end of the horn may need to be sanded smooth or shaved off.
– Do not hold the boiler button down for too long. If the trapped bubbles are too large in size, the experiment will not work.
– As the water heats up from using the boiler, make sure resonance is maintained.
– Make sure the function generator is set to a sine function instead of square wave.
– Search for sonoluminescence at higher transducer voltages than the teachspin manual suggests.
– Confirm sonoluminescence with your eyes before attempted any long exposure photography. The light produced is brighter than one might expect.

Results Summary

The first photograph of sonoluminescence obtained during this experiment was obtained at a peak transducer voltage of 2.29 V, and a driving frequency of 29.519 kHz. The photograph could hardly be interpreted until the contrast was modified on a computer. A variety of photographs were taken using different levels of low background light. In two of these, simultaneous sonoluminescence was observed at both antinodes of the standing wave. These photographs have had their contrast adjusted, and are shown in the figures at the end of this article.

The lifetime of these sonoluminescent bubbles was highly dependent upon the driving amplitude. If the amplitude increased toward the threshold of stability, the bubbles would be much brighter and would only last a few seconds. If the horn amplitude was reduced however, the lifetime of the bubble was approximately one minute. In one case, a single sonoluminescing bubble was observed for approximately four minutes before it dissolved.

By using water at temperatures ranging from approximately to 10 &#176;C to 30 &#176;C, the light intensity dependence on temperature was evident. When the water was close to room temperature, the horn amplitude had to be much closer to the instability threshold for the light to be seen.

To characterize the resonant properties of the cell, the peak transducer voltage was measured at intervals of 10 Hz from below to above the resonant frequency.

$V(f) = A e^{-\left(\frac{f-f_{\text{res}}}{w}\right)^2} + V_0$

Using this gaussian fit, we can calculate the full width half max by finding the frequency at which the curve reaches half of the peak value of $V(f_r)$.

$\Delta f = 141 \pm 7\hspace{1mm} \text{Hz} \hspace{.2in} f_{\text{res}} = 26908.0 \pm 0.8 \hspace{1mm} \text{Hz}$

$\boxed{Q=\frac{f_{\text{res}}}{\Delta f} = 191 \pm 9}$

To qualitatively explore the standing wave at resonance, the hydrophone was used to find the nodes and antinodes along the axis below the ultrasonic horn by measuring pressure. Although there were no convenient mounts which could be used to make depth measurements, the oscillioscope signature from the hydrophone did show the expected resonant structure. When placed near the nodes, the hydrophone voltage dropped to zero, but at antinodes the hydrophone voltage oscillated with the same frequency as the transducer voltage.

Oscillioscope display of hydrophone voltage (top) and transducer voltage (bottom) at the upper antinode. The two waves are very close to being in phase with each other.

Oscillioscope display of hydrophone voltage (top) and transducer voltage (bottom) at the lower antinode. The two signals have a $\pi/2$ phase difference. This phase difference implies that sonoluminescent bubbles at each antinode will emit light with a phase difference of $\pi/2$ as well.

Results and Conclusions

By carefully controlling experimental conditions, sonoluminescence was produced and documented in course of this experiment. The sensitivity to many details is what gives this experiment its reputation of being difficult to conduct. With that said, after enough practice and elimination of mistakes, the Teachspin apparatus can certainly prove to be sufficient in producing sonoluminescence.

In this experiment, sonoluminescence was found at a transducer voltage that was approximately 2x higher than the Teachspin manual suggested it should be. In addition, a quality factor of $Q= 191 \pm 9$ was obtained experimentally, which is twice as large as the manual specified $Q = 95$ for the setup.

Light emission intensity has been seen to relate inversely with water temperature in sonoluminescence. This observation was purely qualitative in nature, but was obvious during the experiment. Additionally, the [1,1,3] resonant mode structure has been confirmed qualitatively by probing acoustic pressure beneath the ultrasonic horn at various depths using the hydrophone.

Possible improvements to this experiment include the use of a photomultiplier tube to characterize the rise time and duration of a sonoluminescent light pulse, and the incorporation of a noble gas to increase sonoluminescent intensity.

References

Steer, W. A. “Sonoluminescence Experiment: Sound Into Light.” Techmind. Web. 30 Mar. 2012. <http://www.techmind.org/sl/>.

Liberati, S., F. Belgiorno, and Matt Visser. “Comment on ‘Dimensional and Dynamical Aspects of the Casimir Effect: Understanding the Reality and Significance of Vacuum Energy’ ” Arxiv. Cornell University Library. Web. 30 Mar. 2012. <http://arxiv.org/abs/hep-th/0010140v1>.

“Sonoluminescence.” Wikipedia, the Free Encyclopedia. Web. <http://en.wikipedia.org/wiki/File:Sonoluminescence.png>.

Teachspin SL100B Sonoluminescence Operation Manual. Kord, John.