Parallelism of half-intercept and delay-time curves

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Problem 11.10

Prove that a half-intercept curve is parallel to the curve of the total delay time (see Figure 11.10a).


Referring to Figure 11.10a, we can write

Figure 11.10a.  Delay-time and half-intercept curves.

[see equations (11.9b)]. Thus is a linear function of with slope . The total delay time is

being constant. If we substitute (see Figure 11.9a) in equation (11.8a), we obtain the result

Thus the total delay-time curve is parallel to the half-intercept time curve and lies above it the distance .

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