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C) A representative plot of pressure amplitude versus distance along the axis as it would be in water or other medium with small attenuation. 2 STRUCTURE OF MEDICAL ULTRASOUND FIELDS / 47 disc diameter D to the sonic wavelength A. The extent of the near field, as it is often defined, and the number of pressure-amplitude maxima and minima along the axis are determined by the quantity Dl A. If DIX >> 1, then the distance to the pressure-amplitude maximum furthest from the vibrating surface is given (in minimally attenuating media) by The quantity z, also is often defined as the distance from the face of the radiator to the point of transition from near field to far field.

The quantity PE is the time-averaged potential energy density (potential energy per unit volume) of the sound field a t the point in question and K E is the corresponding time-averaged kinetic-energy density. 1), the two densities are equal and, therefore, cancel so that pradis constant. 5, the radiation pressure, prad,is positive and equal to p o 2 / 4 p ~a2t velocity nodes (pressure antinodes) and negative with the same magnitude a t pressure nodes (velocity maxima). In a traveling spherical wave, p r o d is constant, typically zero, a t large distances from the center (kr >> I ) but decreases algebraically with decreasing r, and may take on fairly large negative values when kr << 1.

1. Beyond this position, the axial acoustic pressure amplitude begins to vary inversely with the distance from the source, the intensity varies as the inverse square of the distance, and the effective width of the acoustic beam increases. 2a provides a useful, though very simplified, representation of the field from a circular source of uniform velocity amplitude distribution. The near field is shown as a region of uniform cross section while the cross section in the far field increases with distance from the source.

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