An array of air bubbles in a rubber-like material can be made to block the transmission of sound. This finding might help in the design of soundproof walls for music rooms and urban apartments.
The past decade has witnessed growing interest in the fabrication of artificial materials that can interact with waves. Following on from successful efforts to microfabricate photonic crystals, thereby producing novel methods for controlling electromagnetic waves, researchers have started looking for more effective ways to control mechanical waves such as sound waves. When we listen to a symphony, we are detecting acoustic waves in our frequency range of hearing (sonic waves) — from 20 hertz to about 20 kilohertz (middle C has a frequency of 261 Hz). Higher frequencies, spanning 20 kHz to 1 gigahertz, are termed ultrasonic waves, and are commonly used for applications in medical imaging. At higher frequencies still, from about 1 GHz to the terahertz regime, are hypersonic phonons, which carry heat. Writing in Applied Physics Letters, Leroy and colleagues1 describe a new material construct for damping the transmission of ultrasonic phonons.
A photonic (for light), or equivalently phononic (for sound), crystal is an artificially engineered material made of a regularly repeating arrangement of elements that allow impinging waves to undergo destructive interference: waves with frequencies that fall within a range known as the bandgap are prevented from propagating in the material. For destructive interference to occur, the period of the structure must be of the order of the wavelength. This means that, to block sound for human hearing, the periods would be very large, and the overall structure quite unwieldy — metre-sized! In fact, sound attenuation has been serendipitously achieved on Eusebio Sempere's phononic sculpture Órgano, which is on display in the garden of the Juan March Foundation in Madrid (Fig. 1). This structure has a bandgap at around 1.6 kHz, and is made of 3-centimetre-diameter metal rods arranged on a 10-cm-period lattice, fixed on a circular platform of 4 metres diameter2.
But there is another way to block sound: resonance. In 1933, Marcel Minnaert published3 a paper in the Philosophical Magazine, called 'On musical air-bubbles and the sounds of running water', in which he outlined the basic theory of the origin of the sound emitted by an air bubble formed in water. His key insight was that the bubble undergoes radial oscillation (a 'breathing mode') inside the surrounding fluid. Minnaert found that the resonant frequency of the bubble (ω0) depends on the bulk modulus of the air (βair; a measure of a substance's resistance to compression), the density of the water (ρwater) and the radius of the bubble (Rbubble): thus, ω0 = (3βair/ρwater)½/Rbubble.
Interestingly, the low bulk modulus of air (about 10,000 times smaller than that of a typical liquid) results in a low resonant frequency, one that is within the range of human hearing even for quite small bubbles (Rbubble of the order of a millimetre). If, instead of creating bubbles that emit sound, one has a liquid containing a host of randomly arranged bubbles, incident waves of the correct frequency could set each bubble into resonance, thus absorbing the waves' energy and limiting the propagation of sound in the medium. If one could make bubbles of uniform size and place them in a periodic array of the correct spacing, the material would have two independent mechanisms for deterring the propagation of waves: energy absorption through the single-bubble resonance and destructive interference from Bragg scattering of the waves, owing to the periodic bubble array. The trick is to somehow create and fix in place the right sort of bubble array in a liquid. But it is difficult to make bubbles that have uniform size and that, once made, will remain inside a liquid.
In their experiment, Leroy and colleagues1 circumvent this problem by employing a rubber-like material — a soft, castable elastomer called polydimethylsiloxane (PDMS) — in place of the liquid. They used a hard template to create a two-dimensional periodic array of cavities (bubbles) in each of a number of layers of the elastomer, and then stacked the layers to form a three-dimensional array of cavities. The cavities were actually cylinders with an aspect ratio near one, not perfect spheres, but this doesn't affect things much. Because PDMS is not a true liquid, one needs to modify the expression for the Minnaert resonant frequency to take into account its non-zero shear modulus (the material's rigidity). Fortunately, PDMS has a shear modulus only about five times that of the bulk modulus of air, so that the resonant frequency of an air bubble in this soft solid remains low.
Because Leroy et al.1 couldn't precisely align upper and lower bubble layers with one another, the overall stacked structure has some disorder. But it turns out that such stacking disorder doesn't alter the destructive Bragg interference when the incident waves are travelling along the direction perpendicular to the structure surface. By fabricating bubbles with diameters of about 80 micrometres, stacked in layers about 360 micrometres apart, the authors allow the two mechanisms to block the same waves. They find that sound is attenuated by a factor of 1,000 over a bandgap of 0.25 MHz. Their finding shows that, by combining resonance absorption and destructive Bragg scattering, a more compact structure could be used to block sound.
Thus, Leroy and colleagues' simple system paves the way for the development of more complex bubble-based phononic crystals that could yield a broader and deeper (greater attenuation) bandgap than the authors achieved. This could be accomplished by engineering the material to have more than one structural period and bubbles of different sizes. Another possibility is to physically join individual bubbles; this would reduce the system's resonant frequencies and increase the effective damping of the waves and the width of the bandgap.
In future experiments, alignment of the elastomer layers could be obtained by various optical or physical means, providing Bragg interference for waves incident from various angles. Thus, by using different bubble sizes, connecting bubbles within individual layers, varying the spacing between layers and so on4, the soft, bubbly medium proposed by Leroy and colleagues may one day meet the challenges faced by garage bands trying to insulate their sound from their neighbours.
Leroy, V. et al. Appl. Phys. Lett. 95, 171904 (2009).
Martínez-Sala, R. et al. Nature 378, 241 (1995).
Minnaert, M. Phil. Mag. 16, 235–248 (1933).
Feuillade, C. J. Acoust. Soc. Am. 98, 1178–1190 (1995).
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