Traveling wave reflection coefficients

E z) and Em(z) are, respectively, the waves travelling toward the fixed and the moving mirrors and t and r are the amplitude transmission and reflection coefficients. These should not be confused with the transmittance and the reflectance. When theses waves return to the beamsplitter they will be divided again. Some of the light will propagate back toward the source and the rest to the detector. The waves which are detector bound are now,... 

An acoustic wave which is traveling in a medium characterized by an impedance encounters a change of impedance Z at the face of the sample. This change causes the wave to be partially reflected with a complex reflection coefficient r, given by... 

The subscripts 1 and 2 refer to the material the wave travels in and the material that is reflected by or transmitted into, respectively. These equations show that the maximum transmission of ultrasound occurs when the impedances and Z2 of the two materials are identical. The materials are then said to be acoustically matched. If the materials have very different impedances, then most of the US is reflected. The reflection and transmission of ultrasound at boundaries has important implications on the design of ultrasonic experiments and the interpretation of their results. In addition, measurements of the reflection coefficient are often used to calculate the impedance of a material. 

This equation is interesting in that it shows the make up of the forward travelling wave in tube As we would expect, this is partly made up of the forward travelling wave from tube k and partly from some of the backward travelling wave being reflected at the junction. The coefficient of in Equation 11.14 is the amount of that is transmitted into the next tube, k+, and is termed the transmission coefficient. The coefficient of j is the amount of that is reflected... 

Recall fi om our tube model, that the reflection coefficients were originally defined in terms of the ratio of the areas between two adjacent tubes. Equation 11.15 stated that the amount of the forward travelling wave that was reflected back into the tube was given as ... 

We start the LSF analysis by constructing two new transfer functions for the lossless tube. We do this by adding a new additional tube at the glottis, which reflects the backwards travelling wave (whose escape would otherwise cause the loss) into the tube again. As explained in Section 11.3.3, this can be achieved by either having a completely closed or completely open termination. In the closed case, the impedance is infinite, which can be modelled by a reflection coeflBcient value 1, by contrast the open case can be modelled by a coefficient value -1. 

The two intrinsic losses represent the attenuation that occurs in each of the bulk phases. The attenuation through the emulsion will be related to some volume-averaged combination of the two attenuation coefficients. The other losses are due to scattering. Reflectional losses occur when there are differences between the acoustic impedance of the two phases. The reflected sound is not absorbed by the system, but is scattered out of the path of the forward travelling wave and thus lost to the receiver. 

The term exp[iax] in equations (2.47) indicates travel in the positive x-direction, while exp[—iax] refers to travel in the opposite direction. The coefficient A is, then, the amplitude of the incident wave, B is the amplitude of the reflected wave, and F is the amplitude of the transmitted wave. In region III, the particle moves in the positive x-direction, so that G is zero. The relative probability of tunneling is given by the transmission coefficient T... 

Inhomogeneous Media. The inhomogeneities considered here are on the macroscopic rather than microscopic scale. The first topic considered is layered media. To begin with, consider a flat boimdaiy between two media of different acoustic properties. When an acoustic wave traveling through one medium encounters at normal incidence the boimdaiy with another medium, some of the acoustic energy is reflected and some transmitted (12). The sound power transmission coefficient T is given by... 

---