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Acoustical Model of Anisotropy

The anisotropic character of materials relates to those properties that have different values when measurements are made in different directions within the same material. This interactive tutorial explores how sound waves exhibit anisotropic character as a function of grain structure when traveling through a wooden block, which serves as an excellent model for the behavior of light passing through anisotropic crystals.

Appearing in the tutorial window is a virtual block of wood and two stainless steel pinballs positioned near the top and left side of the wooden block. To activate the tutorial, use the mouse cursor to click on the blue Top or Side buttons in order to drive each pinball into the block. When a pinball impacts the wood, a sound wave is generated that traverses the interior of the block. Radio buttons labeled Sinusoidal and Wavefront can be employed to toggle between these two representations of acoustical wave behavior. The speeds at which sound waves travel through the wooden block are proportional to the direction of the wood grain, as explained below.

Isotropic substances display similar physical properties, regardless of the orientation and/or direction from which these properties are measured. In contrast, anisotropic materials have orientation-specific properties that are readily demonstrated by a block of wood in the tutorial. The complex grain structure of wood displays anisotropic behavior because most wood tissues are much stronger in a direction parallel to the grain than across. When the relative humidity changes, wood shrinks and swells to a greater degree across the grain than it does along the length of the grain. Wood is also more easily split or separated along the grain boundaries, but it is more difficult to stretch wood along the grain length than across the grain. Another anisotropic property of wood is the velocity of sound through the porous material, which can be up to three times greater when sound is traveling parallel to the grain as opposed to propagation in a perpendicular direction.

The block of wood illustrated in the tutorial is positioned so that the grain length is traveling from top to bottom. When a stainless steel pinball impacts the block from the top, a standing wave is formed and travels through the wood with loops at the ends of the block and a node in the center. This standing wave acquires a particular pitch or tone (wavelength) that is related to the acoustic velocity of the wave as it travels through the wood. As the wooden block is tapped from the side by the other pinball, another acoustic wave propagates through the wood with a different velocity (and tone). A comparison of the two sound waves reveals that the velocity across the grain is much lower, producing a lower tone having a longer wavelength of lesser frequency. Using hard oak to test this principle, the acoustic frequency along the grain direction is 4000 hertz, while across the grain the frequency is reduced to 2500 hertz. In this case, the compressive sound wave travels nearly twice as fast with the grain as opposed to against the wood grain.

Contributing Authors

Robert T. Sutter and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.



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