Forward traveling waves

Figure 11.8 A uniform tube with forwards travelling wave, +, and backwards travelling wave u...

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... 

The effect of a sound source in the middle of the vocal tract is to split the source such that some sound travels backwards towards the glottis while the remainder travels forwards towards the lips. The vocal tract is thus effectively split into a backward and forward cavity. The forward cavity acts a tube resonator, similar to the case of vowels but with fewer poles as the cavity is considerably shorter. The backwards cavity also acts as a further resonator. The backwards travelling source will be reflected by the changes in cross sectional area in the back cavity and at the glottis, creating a forward travelling wave which will pass through the constriction. Hence the back cavity has an important role in the determination of the eventual sound. This back cavity acts as a side resonator, just as with the oral cavity in the case of nasals. The effect is to trap sound and create antiresonances. Hence the back cavity should be modelled with zeros as well as poles in its transfer function. 

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 ... 

In order to study amplification (lasing action), it is appropriate to adopt a semiclassical description of the field and assume as boundary conditions a forward-travelling wave with a given initial value e(0,0) of the field amplitude . Removing the arbitrary initial phase of the field, it is possible to eliminate the Bloch vector from the combined equations (12) (13). Under steady-state conditions, as E becomes t-independent, one can introduce a reduced amplitude... 

Crossed field ampHlier (CFA) Radial or linear traveling wave amplifier where radial or transverse DC accelerating electric fields are perpendicular to axial or longitudinal DC magnetic fields, respectively. Crossed field devices (CFD) Radial or linear forward traveling wave amplifier or backward wave oscillator where radial or transverse DC accelerating electric fields are perpendicular to axial or longitudinal... 

Mode voltage (voltage in a modal domain) and modal forward traveling wave (forward traveling wave in a modal domain) are defined as follows ... 

For simplicity, assume that a forward traveling wave e on line 1 arrives at node 1 at t 0 Then, node voltage is calculated by... 

The earlier solution is known as a wave equation and shows a behavior of a wave traveling along the x-axis by the velocity Cq. It should be clear that the value of functions Cf, e Ej, and E does not vary if x-Cof=constant and x + Cot = constant. Since Cj and Ef show a positive traveling velocity, they are called "forward traveling wave" ... 

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. 

Again, as expected, in Figure 5 there is an excess of surfactant near the rear stagnation ring due to surface convection towards that point. Forward from that location, however, there is also a depletion relative to equilibrium adsorption. This is caused by the traveling wave in the rear bubble profile as demonstrated in Figure 2 and in Figure 7 to follow. 

The person can create a forcing function (i.e. source) input to the system by moving their hand in a repetitive fashion. In doing so, a series of pulses will form and travel forwards down the rope towards the wall, and these pulses will create a travelling wave, the frequency of which is dictated by the hand movement. When this forward travelling... 

Usually a traveling wave tube means a forward wave tube. In the vacuum tube, the electron beam and forward waves interact with each other. There is a vacuum tube in which the electron beam interacts with backward waves. This type of tube is termed the backward wave tube. The backward wave tube is inherently highly regenerative (built-in positive feedback) therefore, it is usually an oscillator. Such an oscillator is termed a backward wave oscillator (BWO). The BWO has a traveling wave structure inside, but usually it is not called a traveling wave tube. Details of a BWO are presented in Chap. 6.4.3. The oscillation frequency of a BWO is dominated by the electron speed, which is determined by the anode voltage. Therefore, a BWO is a microwave frequency voltage controlled oscillator (VCO). 

Characteristic impedance Ratio of a transmission line voltage of a forward voltage traveling wave to the accompanying transmission line current of a forward current traveling wave. 

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