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Wednesday, July 18, 2012

Fundamentals of Acoustic Propagation on Ultrasound

Ultrasound is a sound wave characterized by such parameters as pressure, particle (or medium) velocity, particle displacement, density, and temperature. It differs from a sound wave in that its frequency is higher than 20×103 cycles per second or 20 kHz (kilohertz). The audible range of human ear is from 20 Hz to 20 kHz. Because ultrasound is a wave, it transmits energy just like an electromagnetic wave or radiation. Unlike an electromagnetic wave, however, sound requires a medium in which to travel and thus cannot propagate in a vacuum.To better visualize how the sound propagates through a homogeneous medium, the medium can be modeled as a three-dimensional matrix of elements, which may represent molecules, atoms, or elemental particles, separated by perfect elastic springs representing inter element forces. To simplify the matter even more, only a two-dimensional lattice  , in which the elements are represented by spheres. When a particle is pushed to a distance from its neutral position, the disturbance or force is transmitted to the adjacent particle by the spring. This creates a chain reaction. If the driving force is oscillating back and forth or sinusoidally,the particles respond by oscillating in the same way. The distance,U,traveled by the particle in the acoustic propagation is called particle or medium displacement, usually in the order of a few tenths of a nanometer in water. The velocity of the particle oscillating back and forth is called particle or medium velocity,u, and is in the order of a few centimeters per second in water. It must be noted that this velocity is different from the rate at which the energy is propagating through the medium.

The velocity at which the ultrasound energy propagates through the medium is defined as the phase velocity or the sound propagation velocity,c. In water, c=1500 m/s.The sound velocity is much faster than the particle velocity. Although the particle has only moved a short distance, the perturbation has already been transmitted to other particles over a much longer distance,U′. As a sinusoidal disturbance is propagated into a liquid medium, regions of medium compression and rarefaction will be produced, . The displacement of the particles,U, is in the same directionas the direction of wave propagation,X This type of wave is called a longitudinal or compressional wave.The particle displacement in the rarefaction region is the largest and it is the smallest in the compression. 

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