Acoustic response function

Si is the laminar flame velocity, the function Z(co) is the heat response function Equation 5.1.16, whose real part is plotted in Figure 5.1.10. The function f(r, giJ is a dimensionless acoustic structure factor that depends only on the resonant frequency, a , the relative position, r, of the flame, and the density ratio Pb/Po-... 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

Fig. 13.17 shows the structure and principle of a T-bumer, as used to measure the response function of propellants. Two propellant samples are placed at the respective ends of the T-burner. The burner is pressurized with nitrogen gas to the test pressure level. The acoustic mode of the burning established in the burner is uniquely determined by the speed of sound therein and the distance between the burning surfaces of the two samples. When the propellant samples are ignited, pressure waves travel from one end to the other between the burning surfaces of the samples. When a resonance pressure exists for a certain length of the T-bumer, the propellant is sensitive to the frequency. The response function is determined by the degree of amplification of the pressure level. 

The Eulerian finite difference scheme aims to replace the wave equations which describe the acoustic response of anechoic structures with a numerical analogue. The response functions are typically approximated by series of parabolas. Material discontinuities are similarly treated unless special boundary conditions are considered. This will introduce some smearing of the solution ( ). Propagation of acoustic excitation across water-air, water-steel and elastomer-air have been computed to accuracies better than two percent error ( ). In two-dimensional calculations, errors below five percent are practicable. The position of the boundaries are in general considered to be fixed. These constraints limit the Eulerian scheme to the calculation of acoustic responses of anechoic structures without, simultaneously, considering non-acoustic pressure deformations. However, Eulerian schemes may lead to relatively simple algorithms, as evident from Equation (20), which enable multi-dimensional computations to be carried out in a reasonable time. 

For heterogeneous propellants, the current situation is much less satisfactory. The complexity of the combustion process was discussed in Section 7.7. To employ a result like equation (66) directly is questionable, although attempts have been made to evaluate parameters like A and B of equations (67) and (68) from complicated combustion models for use in response-function calculations [81], [82]. Relatively few theories have been addressed specifically to the acoustic response of heterogeneous propellants [82]. Applications of time-lag concepts to account for various aspects of heterogeneity have been made [60], [83], a simplified model—including transient variations in stoichiometry—has been developed [84], and the sideways sandwich model, described in Section 7,7, has been explored for calculating the acoustic response [85], There are reviews of the early studies [7] and of more recent work [82],... 

Here, p(t) is the electric signal applied to the transducer at time t, gi(t) is the electro-acoustic conversion function of the transducer, g2(t) is the acoustic-electro conversion function of the transducer, and h(t) are the response functions of the sample. The Fourier transformation of p(t), gi(t), g2(t) and h(t) are defined as follows ... 

Here, p is the magnitude of pressure fluctuation, c is the speed of sound,/is the frequency of acoustic wave, k = Inf/c is the wave number, z is the axial direction, p is the fluid viscosity, p is the density, R is the radius of tube, v is the kinematic viscosity, and / is the Bessel function. The frequency response function H(f) from Eq. 27 is used to determine the frequency response of the shear stress sensor as... 

Acoustic emission caused by single particle impact is reasonably well understood. It is possible to quantitatively analyze acoustic emission signals to predict particle size. The analysis is based on a deconvolution of the acoustic emission source function from the measured acoustic emission signal. The measured acoustic emission signal V(t) is a convolution of the acoustic source S(t), the propagation function through the metal plate G(t), and the detector response function D(t), where = represents convolution ... 

The effects of pyrethroids on acoustic startle response (ASR) were examined to detect the effects on sensorimotor function. Pyrethroids show various effects on ASR (Table 3). Crofton and Reiter reported that non-cyano pyrethroids showed no effect on the latency, while they increased the amplitude. a-Cyano pyrethroids showed increase or no change on the latency, while various effects on the amplitude were observed [30, 31]. Fenvalerate showed effects similar to non-cyano pyrethroids. In studies by Hijzen et al. [32, 33], the results of permethrin and deltamethrin on the amplitude were consistent with the findings by Crofton and Reiter, but cypermethrin induced contradictory effects. NAK 1901 showed similar effects to other non-cyano pyrethroids. The reason for the inconsistency of effects of pyrethroids on startle response remains unsolved. 

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