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An Audible Demonstration of the Speed of Sound in Bubbly Liquids Preston S An audible demonstration of the speed of sound in bubbly liquids Preston S. Wilson and Ronald A. Roy Citation: American Journal of Physics 76, 975 (2008); doi: 10.1119/1.2907773 View online: http://dx.doi.org/10.1119/1.2907773 View Table of Contents: http://scitation.aip.org/content/aapt/journal/ajp/76/10?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Correction: “Bubbles that Change the Speed of Sound” (Phys. Teach.50, Nov. 2012)page 459 Phys. Teach. 51, 72 (2013); 10.1119/1.4775519 Bubbles that Change the Speed of Sound Phys. Teach. 50, 458 (2012); 10.1119/1.4758141 Interaction between acoustic and non-acoustic mode in a bubbly liquid AIP Conf. Proc. 1433, 531 (2012); 10.1063/1.3703243 A mechanism stimulating sound production from air bubbles released from a nozzle J. Acoust. Soc. Am. 123, EL126 (2008); 10.1121/1.2908198 Sound–ultrasound interaction in bubbly fluids: Theory and possible applications Phys. Fluids 13, 3582 (2001); 10.1063/1.1416502 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.83.205.78 On: Mon, 11 May 2015 21:48:30 APPARATUS AND DEMONSTRATION NOTES Frank L. H. Wolfs, Editor Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627 This department welcomes brief communications reporting new demonstrations, laboratory equip- ment, techniques, or materials of interest to teachers of physics. Notes on new applications of older apparatus, measurements supplementing data supplied by manufacturers, information which, while not new, is not generally known, procurement information, and news about apparatus under development may be suitable for publication in this section. Neither the American Journal of Physics nor the Editors assume responsibility for the correctness of the information presented. Manuscripts should be submitted using the web-based system that can be accessed via the American Journal of Physics home page, http://www.kzoo.edu/ajp/ and will be forwarded to the ADN editor for consideration. An audible demonstration of the speed of sound in bubbly liquids ͒ Preston S. Wilsona Mechanical Engineering Department and Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78712-0292 Ronald A. Roy Department of Aerospace and Mechanical Engineering, Boston University, Boston, Massachusetts 02215 ͑Received 5 January 2007; accepted 18 March 2008͒ The speed of sound in a bubbly liquid is strongly dependent upon the volume fraction of the gas phase, the bubble size distribution, and the frequency of the acoustic excitation. At sufficiently low frequencies, the speed of sound depends primarily on the gas volume fraction. This effect can be audibly demonstrated using a one-dimensional acoustic waveguide, in which the flow rate of air bubbles injected into a water-filled tube is varied by the user. The normal modes of the waveguide are excited by the sound of the bubbles being injected into the tube. As the flow rate is varied, the speed of sound varies as well, and hence, the resonance frequencies shift. This can be clearly heard through the use of an amplified hydrophone and the user can create aesthetically pleasing and even musical sounds. In addition, the apparatus can be used to verify a simple mathematical model known as Wood’s equation that relates the speed of sound of a bubbly liquid to its void fraction. © 2008 American Association of Physics Teachers. ͓DOI: 10.1119/1.2907773͔ I. INTRODUCTION a drinking glass filled with a “frothy liquid” produces a dull sound. Perhaps inspired by his former laboratory assistant,2 The interaction of sound and bubbles has been studied in Rayleigh published a paper in 1917 that described the sound 3 modern science for almost 100 years and has been part of produced by water boiling in a tea kettle. In 1933, Minnaert human consciousness for many hundreds of years, perhaps studied the sounds produced by running water, such as the 4 longer. It is a scientifically interesting and complex phenom- flowing stream and the crashing of ocean waves. The latter enon with a long and diverse history, yet our understanding two studies both introduced relationships between the size of of the phenomenon is still incomplete. Part of the intrigue a bubble and its period of oscillation with water as the host comes from the fact that minute parameter changes in a bub- medium, but Rayleigh considered steam bubbles while Min- bly fluid can have large and unexpected effects. For example, naert considered air bubbles. consider a column of water contained within a rigid tube. The acoustics of bubbly liquids now has a number of im- The addition of just a small number of bubbles, representing portant practical applications. These include a variety of in- as little as 0.1% by volume, can transform the once simple dustrial processes utilizing multiphase flow,5 microfluidic medium into a highly dispersive and nonlinear one, with a manipulation,6 and the design of nuclear reactor containment speed of sound less than 20% of the speed of sound in the systems.7 In the ocean, various acoustic techniques are used host medium. That corresponds to a 4 parts in 5 change in in conjunction with oceanic bubble populations to make the speed of sound for a 1 part in 10 000 change in the measurements relevant to meteorology, chemical oceanogra- density. It is the added compressibility of the gas phase that phy, marine fluid dynamics, and marine biology.8 By shroud- causes the reduction of the speed of sound. ing propellers and hulls with man-made bubble screens, un- The early scientific work on the acoustics of bubbles was wanted noise produced by ships and submarines is reduced.9 motivated primarily by the desire to understand certain man- Bubbles are used in medical applications to enhance ultra- made and natural curiosities. In 1910, a paper was published sound imaging,10 hemostasis,11 and therapy.12 by Mallock1 that sought to explain the fact that when struck, Both theory and measurement reveal that for acoustic ex- 975 Am. J. Phys. 76 ͑10͒, October 2008 http://aapt.org/ajp © 2008 American Association of Physics Teachers 975 This article is copyrighted as indicated in the article. Reuse of AAPT content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.83.205.78 On: Mon, 11 May 2015 21:48:30 citation frequencies that are close to the individual bubble If the bubble radius is perturbed, equilibrium is lost and resonance frequency, the acoustic attenuation within a bub- oscillations occur. The alternating compression and expan- bly liquid is measured in tens of decibels per centimeter, and sion of the bubble is due to the transfer of energy between that the sound speed can vary from as little as 20 m/stoas the inertia provided by the surrounding liquid and the com- much as 10 000 m/s, which is supersonic relative to bubble- pressibility of the gas inside the bubble. For the frequency free water. In the littoral ocean environment, this behavior is range between 100 and 1200 Hz and a bubble size of about a dominant obstacle for effective sonar operation because 1 mm, it is sufficient to assume lossless conditions within the bubbles and bubble clouds are produced in abundance by bubble, but dissipative effects are important in other 20 breaking waves. The acoustic contrast provided by bubbly regimes. At a hydrostatic pressure Pϱ, the compressibility liquid causes sound to be scattered from bubble clouds, and of the gas inside the bubble leads to an effective stiffness 21 hence naval sonar and mine hunting operations are hindered. 12␲¯a␯Pϱ. The bubble behaves acoustically like a pulsating Bubbles are also a source of ambient noise in the ocean. sphere and radiates sound uniformly in all directions. Since Rain drops, spray from breaking waves, and even snow can the bubble size is always much smaller than the resulting entrain bubbles when they impact the ocean surface. The acoustic wavelength, the low frequency limiting value of the impact deforms the ocean surface and creates an air cavity. acoustic radiation reactance can be used to define an effec- 3 When this cavity closes, a bubble is formed and a second tive mass, known as the radiation mass 4␲¯a ␳ᐉ, where ␳ᐉ is impact that occurs when the air cavity closes causes the the liquid density. The bubble’s resonance frequency is then 13–15 bubble to oscillate and radiate sound. Breaking waves given by the square root of the stiffness to mass ratio, or produce clouds composed of large numbers of bubbles that 1 3␯Pϱ oscillate collectively and radiate sound. These bubble clouds ␻ ͱ ͑ / ͒ ͑ ͒ 0 = radians sec . 2 are responsible for part of the ambient noise in the ocean ¯a ␳ᐉ 16 below about 1000 Hz. 4 The physics of bubble acoustics has been the subject of This relation was first derived by Minnaert in 1933, al- previous “Apparatus and Demonstration Notes” within this though via a different methodology. Minnaert considered journal,17–19 but the apparatus described here complements bubbles in the size range between 3 and 6 mm, and con- and expands upon the previous work. The apparatus consists cluded that the period of oscillation would be small com- of a transparent PVC pipe about 0.5 m in length. Air bubbles pared to the time required for the heat of compression to be are injected at the bottom of the water-filled tube and a hy- conducted away. The bubble was considered to be undergo- ␯ drophone is used to detect the resulting sounds.
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