The equations derived earlier for the probe voltages (VP1 and VP2) exhibit a standing wave pattern, which can clearly be observed in your node voltage graphs for both cases of even and odd mode excitations. As you already saw in Tutorial Lesson 1, the exponential term:
<math> e^{-j2\beta L} = e^{-j2 \frac{2\pi}{\lambda_g} L } = e^{-j j2\pi f \frac{4\pi2L}{c} \sqrt{\epsilon_{eff}} fL } </math>
determines the frequency variation of the voltages, which have a periodic nature.Since ε<sub>eff</sub> = 1 in this case, the period is c/(2L) = 3×10<sup>8</sup> / (2×0.075) = 2GHz.
βL = 2πL/λ<sub>g</sub> = 2π√(ε<sub>eff</sub>)(f.L)/c