Backward 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... 

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. 

On the contrary, and E are backward traveling waves, which means the waves travel in the direction of -x, that is, the traveling velocity is negative ... 

Resistance-terminated line A resistance is equivalent to a semi-infinite line whose surge impedance is the same as the resistance as explained in Section 1.6.2.1 and in Figure 1.33. If the surge impedance of the semi-infinite line is taken to be the same as that of the line to which the resistance is connected, then a backward traveling wave + ct) = ej, is to be placed on the semi-infinite line ... 

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