In view of Eq. (1), in a traveling wave the potential and kinetic energies are in phase: they are both maximal
together, and they vanish together too. Specifically, at a crest or a trough the kinetic energy vanishes as the string
element is momentarily stationary, and the potential energy of the string element vanishes because the string element
is horizontal. At zero displacement both are maximal, as both the string transverse velocity and the string’s slope
are maximal. The total mechanical energy of the string element therefore oscillates, as indeed should be expected as
energy is transported with the wave along the string.
In view of Eq. (1), in a traveling wave the potential and kinetic energies are in phase: they are both maximal
together, and they vanish together too. Specifically, at a crest or a trough the kinetic energy vanishes as the string
element is momentarily stationary, and the potential energy of the string element vanishes because the string element
is horizontal. At zero displacement both are maximal, as both the string transverse velocity and the string’s slope
are maximal. The total mechanical energy of the string element therefore oscillates, as indeed should be expected as
energy is transported with the wave along the string.
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