Figure 11.

Models of combinations of two waves [a modal wave M(x) = A_M sin(k_Mx) and a traveling wave T(x) = A_T e^−jk_Tx], with varied magnitudes and spatial frequencies. The left-most panel with its two vertically aligned plots describes the spatially varying magnitude and phase angle of six basic waves M(x) and T(x) with a closed set of parameters: A_T = 1 (horizontal dotted line in magnitude plot); A_M = {0.5, 1, 2, 4} (four solid lines with symbols in magnitude plot), and either k_T = k_M (solid dotted line in the phase angle plot) or k_T = 4k_M (gray dotted line in the phase angle plot). The two right-hand panels describe the spatial variations in displacement magnitude and phase angle predicted by various combinations of one of four modal wave patterns M(x) with one of two traveling waves T(x) (middle panel: k_T = k_M, right-most panel: k_T = 4k_M). The top plot of each panel illustrates the variation in the wave magnitudes as k_Mx and k_T x (plotted on the abscissa) vary. The bottom plot of each panel illustrates the spatial variations in the phase angle of the waves.