Ultrasonic attenuation coefficient

Approximate Ultrasonic Attenuation Coefficient, Speed, and Characteristic Impedance for Water and Selected Tissues at 3.5 MHz... 

In practice ultrasound is usually propagated through materials in the form of pulses rather than continuous sinusoidal waves. Pulses contain a spectrum of frequencies, and so if they are used to test materials that have frequency dependent properties the measured velocity and attenuation coefficient will be average values. This problem can be overcome by using Fourier Transform analysis of pulses to determine the frequency dependence of the ultrasonic properties. 

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 nr1) where 1 Np = 8.686 dB. 

Each echo has traveled a distance twice the cell length d further than the previous echo and so the velocity can be calculated by measuring the time delay t between successive echoes c = 2d/t. The cell length is determined accurately by calibration with a material of known ultrasonic velocity, e.g. distilled water 2d = cw.tw (where the subscripts refer to water). The attenuation coefficient is determined by measuring the amplitudes of successive echoes A = A0e-2cxd, and comparing them to the values determined for a calibration material. A number of sources of errors have to be taken into account if accurate measurements are to be made, e.g., diffraction and reflection (see below). 

Like the ultrasonic velocity and attenuation coefficient, the acoustic impedance is a fundamental physical characteristic which depends on the composition and microstructure of the material concerned. Measurements of acoustic impedance can therefore be used to obtain valuable information about the properties of materials. 

Determining the droplet size distribution of an emulsion by ultrasonic spectrometry involves two steps. First, the ultrasonic velocity and (or) attenuation coefficient of the emulsion is measured as a function of the frequency — preferably over as wide a range as possible. Second, the experimental measurements are compared with theoretical predictions of the ultrasonic properties of the emulsion, and the droplet size distribution providing the best fit between theory and experiment is determined. 

A wave can be characterized by an amplitude, frequency, and wavelength which may change with time or distance traveled from the source. We can express both the storage and loss properties of a sonic wave moving in a material concisely as the real and imaginary parts of a complex wavenumber k = co/c + ia, where c is the speed of sound, co is the angular frequency (=2 Jt/),/is frequency, / = V - 1, and a is the attenuation coefficient. Ultrasonic properties are often frequency dependent so it is necessary to define the wavelength at which k is reported. The dependency of k on frequency is the basis of ultrasonic spectroscopy. 

Ultrasonic velocity has been almost exclusively measured in ultrasonic studies of fat crystallization, but the attenuation coefficient also can reveal interesting information. As the sound wave passes, the fluid is alternately compressed and rarefied which results in the formation of rapidly varying temperature gradients. Heat energy is lost because the conduction mechanisms are inefficient (thermal losses) and together with molecular friction (viscous losses) cause an attenuation of the sound given by classical scattering theory (5) ... 

The effect of ultrasonic degassing of liquid metal on the quality of ingots manifests itself by increased density, decreased coefficient of ultrasonic attenuation, and increased ductility at temperatures of plastic deformation. The data on the ductility of a flat-shaped ingot (1700 x 300 mm) from an AMg6 grade alloy at the temperature of hot deformation of 400 °C are given in Table 10. 

The two gray-shaded areas in Figure 2.12 mark two frequency bands typical for ultrasonic studies on sediment cores (50 - 500 kHz) and sediment echosounder surveys (0.5 - 10 kHz). They are displayed in order to point to one characteristic of acoustic measurements. Attenuation coefficients analyzed from ultrasonic measurements on sediment cores cannot directly be transferred to... 

An ultrasonic measuring system was developed to measure the attenuation coefficient/loss factor of car-tyre rubber samples as a function of the temperature between about -40°C and 150°C. These measurements were performed on sample disks of vulcanised rubber having a diameter of 60 mm. and a thickness of 13 mm. 

Anisotropic Glnzburg-Landau theory for coupled s-wave and d-wave order paraneters Is used to analyze the unique themo namlc and transport properties of the new La2 jj(Ba,Sr) CuO and S P ° 4uctors. This simple phenomenological approach Is used to explain the prevalence of the large Sommerfeld coefficients of the specific heat, the existence of multiple specific heat anomalies, the ultrasonic attenuation peak, and model the anisotropic critical field data as observed In oriented samples. 

The primary measurable ultrasonic parameters of a material are velocity, c, and attenuation coefficient, a, defined as follows ... 

Whichever mefliod is selected, certain practical considerations are essential to making good measurements in food emulsions. The ulfrasonic properties of flie components in food emulsions are particularly sensi tive to temperature and therefore it is usually impor tant to control the measurement temperature carefully (i.e., 0.2 ms j or better). At approximately 18°C, coil = C water and so the ultrasonic technique becomes relatively insensitive to oil concentration (10). At higher and lower temperatures, ultrasonic measurements become increasingly independent on concentration because C qJi—C water I increases. It may, therefore, be pos sible to enhance the sensitivity of an ultrasonic analysis by carefully selecting the temperature at which the measurements are carried out. The attenuation coefficient is typically less dependent on temperature than is the ultrasonic velocity and may be a more reliable parameter to measure in situations when thermal control is poor (e.g., on-line measurements). 

The attenuation coefficient in the flocculated emulsion is lower at low frequencies and higher at high frequencies than that of the nonflocculated emulsions. The decrease in attenuation at low frequencies on flocculation as a result of the thermal overlap effects mentioned earlier, whereas the increase at high frequencies results from increased scattering of ultrasound by the floes. The same ultrasonic spectroscopy technique has been used to study the disruption of floes in a shear field (38). As the emulsions are exposed to higher shear rates the floes become disrupted and their attenuation spectra become closer to that of nonflocculated droplets. 

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