Decomposition of wave into upward and downward ...

  1. the error is in phase at one time and out of phase at other.
  2. It looks like we have soft relfection at one boundary and hard reflection at the other boundary
  3. The first row represents

    \(2cos(kz-\omega t) \)

    this equation represents upward moving waves. Simply at constant phase

    \(kz-wt=constant\)

    by differentiating it, we get

    \(kdz=wdt\)

    , so

    \(w=dz/dt=w/k\)

    , or you might thing this way that at constant phase

    \(kz-wt=constnat\)

    , then if time increase, then z must also increases which means upward motion.
  4. the second row represents

    \(2cos(kz-\omega t) exp(-z/H) \)