## Ultrasonic Properties Of Materials

The use of ultrasound for monitoring food processing operations relies on the knowledge or measurement of the ultrasonic properties of the material being tested. The three most important ultrasonic properties are the velocity at which an ultrasonic wave propagates through a material, the extent to which the wave is attenuated, and the acoustic impedance (which determines the amount of ultrasound reflected from a boundary between two materials). Ultrasonic velocity. The velocity (c) at which an ultrasonic wave travels through a material is related to its physical properties by the following equation.

Here E is the appropriate elastic modulus (which depends on the physical state of the material and the type of wave propagating) and p is the density. The less dense a material or the more resistant it is to deformation the faster an ultrasonic wave propagates. Usually, differences in the elastic moduli of materials are greater than those in density and so the ultrasonic velocity is determined more by the elastic moduli than by the density. This explains why the ultrasonic velocity of solids is greater than that of fluids, even though fluids are less dense [7]. The modulus used in the above equation depends on the physical state and dimensions of the material being tested. For bulk solids the appropriate modulus is K+4G/3, where K is the bulk modulus and G is the shear modulus, for solid rods it is Young's modulus, Y. (A rod is a material which has a diameter much smaller than the wavelength of ultrasound, i.e., d «)J20). For liquids and gasses the appropriate modulus is the bulk modulus, which is the reciprocal of the adiabatic compressibility k. Shear waves will propagate through solids (E=G) but are highly attenuated in liquids and gasses and do not usually travel far enough to be detected. The ultrasonic velocity is determined by measuring either the wavelength of ultrasound at a known frequency (c = Xf), or the time taken for a pulse of ultrasound to travel a known distance (c = d/t).

Attenuation coefficient. As an ultrasonic wave propagates through a material its amplitude decreases, i.e., the wave is attenuated. The major sources of attenuation by a material are adsorption and scattering. Adsorption is due to mechanisms which convert some of the energy stored as ultrasound into other forms and ultimately into heat, e.g., viscosity, thermal conduction and molecular relaxation [8]. Scattering is important in heterogeneous materials, and occurs when an ultrasonic wave encounters a discontinuity (e.g. a particle, crack or void) and is scattered in directions which are different from that of the incident wave. Unlike adsorption the energy is still stored as ultrasound, but it may not be detected by a receiver in the forward direction because its propagation direction and phase have been altered. The attenuation coefficient a of a material has units of Nepers per meter (Np rrr1) when defined by the following equation:

Here A is the amplitude of the wave, and x is the distance traveled. The attenuation coefficient is determined by measuring the dependence of the amplitude of an ultrasonic wave on distance and fitting the measurements to the above equation. The attenuation is often given in units of decibels per meter (dB rrr1) where 1 Np = 8.686 dB.

Acoustic Impedance. The acoustic impedance (Z = pc) determines the proportion of an ultrasonic wave reflected from a boundary between two materials. When a plane ultrasonic wave is incident on a plane interface separating two materials of different acoustic impedance it is partly reflected and partly transmitted (Figure 1). The ratios of the amplitudes of the transmitted (At) and reflected (Ar) waves to that of the incident wave (AO are called the transmission (T) and reflection coefficients (R), respectively.

A, |
2 Zl |

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