"average" wave          "envelope" wave
-------------------------------------------------------------------
                                    15                      13
 angular freq       3.748653120 x 10        1.865001552 x 10
    (rad/s)

                                    7                       4
 wavenumber         1.902196404 x 10        9.651221472 x 10
    (rad/m)

                                     8                       8
 velocity     vp =  1.970697196  x 10       1.932399497  x 10   = vg
    (m/s)

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