The Dome of Silence — For Real

Long story short: scientists have devised a way to shield objects from sound, preventing its reflection.

No echoes = acoustic invisibility.

Here's an article about the new technology from the January 19, 2008 print issue of The Economist.

Sound reflections

How to stop echoes giving you away

In Greek mythology, Echo was a mountain nymph who lost her voice and was condemned to repeat only the words of others. Now science is poised to silence the sprite completely. A group of physicists, led by Steven Cummer of Duke University in North Carolina, has devised plans for a cloak that would shield objects from sound, preventing its reflection. Such a device could be used to hide submarines.

Sonar, the technique employed to detect subs, uses a transmitter to emit a pulse of sound—usually a distinctive “ping”—and a receiver to listen for its reflection. That reflection indicates the presence of an object and the time that elapses between the sound's being emitted and its being detected indicates how far away it is. A second ping allows the object's direction, speed and location to be calculated.

Dr Cummer, however, has devised a plan to surround a submarine with a shell that directs sound waves to flow around it as though the vessel were not there. The proposal relies on two properties of the material used to make the shield—its density and its “bulk modulus”, a measure of its springiness. It should be possible to tailor these so that sound waves are bent such that no echo results. The design would also avoid absorbing sound, ensuring no acoustic “shadows” were cast.

Dr Cummer's method, reported in the current issue of Physical Review Letters, is akin to an existing design for an invisibility cloak that would work for light waves, proposed by Sir John Pendry of Imperial College, London. (Sir John is also one of the authors of the new paper.) Yet the acoustic version has a distinct advantage over its optical counterpart. Making an invisibility cloak would be tricky because the device would work only at certain wavelengths. An aeroplane shrouded in such kit might be invisible to the human eye, for example, but would be picked up readily by radar, which works at radio wavelengths.

An acoustic cloak, however, would work for a wider range of wavelengths, making it far harder to spot. That is possible because light and sound are rather different sorts of waves. As Einstein observed, light in a vacuum travels at the greatest speed possible, around 300m metres a second. Even when it is slowed by air and water, its progress usually remains close to this limit. That means light must obey the rules of Einstein's special theory of relativity. When light is bent by an invisibility cloak, certain components of the wave are allowed to stretch the laws of physics and travel faster than the nominal speed of light, but only under strict conditions. The energy and the information that the wave carries, for example, cannot exceed the speed of light. The effect is to narrow the range of wavelengths that can be bent by an optical shroud.

Sound, meanwhile, travels at a sedate 300 metres a second. Because this is a million times shy of the relativistic limit, the behaviour of sound waves is not restricted in the same way. Under non-relativistic conditions, many different wavelengths can be bent simultaneously by the same acoustic shield, making it far more effective at concealing an object.

It was unrequited love that made the Echo of Greek mythology fade away until only her voice remained. Although Dr Cummer and his colleagues are still some way from transforming their design into a working device, they reckon precisely engineered materials may soon erase her final utterances.

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Here's a January 11, 2008 story in the Physics News Update with more about the work.

Acoustic Cloaking

Computer simulations and the use of wave scattering theory have demonstrated that, contrary to earlier predictions, it should be possible to produce a 3-dimensional material shell which is invisible to sound waves, analogous to “optical cloaking,” the process in which light waves are guided around an object and then refocused on the far side and in the same direction (with no reflected light to betray position) so as to make the object seem invisible. Full optical cloaking has not been achieved yet, but researchers expect to be able to do it.

Can the same thing be done with sound waves? In principle there is no reason why it couldn’t be done. The leader of a group of scientists examining this issue, Steven Cummer at Duke University, says that many of the principles that pertain to the channeling of light waves around an object also apply to sound waves. To be sure, there are differences. Sound waves oscillate in the direction of their motion while the electric and magnetic fields composing light waves oscillate perpendicularly to the wave motion. In the optical case, cloaking will require a material (actually a meta-material) tailored, highly anisotropic (varying widely according to the direction through the material) index of refraction.

In practice, the index of refraction for electromagnetic waves depends on the permittivity, a measure of the material's response to an applied electric field, and permeability, its response to an applied magnetic field (for an account of the demonstration of negative-index materials, see http://www.aip.org/pnu/2000/split/pnu476-1.htm). The acoustic equivalent of these two parameters are the mass density and the bulk modulus (the springiness) of the background fluid (usually air or water) in which the object sits. Cummer (919-660-5256, cummer@ee.duke.edu) says that in the short run acoustic cloaking might be more practical than optical cloaking.

A limitation of electromagnetic cloaking, he says, is that it requires portions of the wave to move faster than the speed of light (in full accordance with special relativity); this can be done for very limited frequency ranges but not for wider ranges, limiting the applicability of optical cloaking. This limitation does not apply to sound waves moving through matter. Furthermore, the acoustic properties of most materials means that sound waves might not be absorbed as readily in acoustic cloaking as light waves are absorbed in optical cloaking (in which case the cloaking would be something less than perfect).

Applications of acoustic cloaking come easily to mind: hiding submarines from sonar, for example. Another potential practical application might be in architecture, where acoustic considerations (reducing noise) might not have to be sacrificed in the interest of structural integrity. Among Cummer’s collaborators are David Smith of Duke (one of the early pioneers in the field of negative-index materials) and John Pendry of Imperial College (the early theorist of negative-index studies).

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Got it?

Good.

Now here's the abstract of the Physical Review Letters publication.

Scattering Theory Derivation of a 3D Acoustic Cloaking Shell

Through acoustic scattering theory we derive the mass density and bulk modulus of a spherical shell that can eliminate scattering from an arbitrary object in the interior of the shell—in other words, a 3D acoustic cloaking shell. Calculations confirm that the pressure and velocity fields are smoothly bent and excluded from the central region as for previously reported electromagnetic cloaking shells. The shell requires an anisotropic mass density with principal axes in the spherical coordinate directions and a radially dependent bulk modulus. The existence of this 3D cloaking shell indicates that such reflectionless solutions may also exist for other wave systems that are not isomorphic with electromagnetics.