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Real/scalar waves and vector waves, commonly called longitudinal and transverse waves. The two waves are the scalar wave and the vector wave of a Quaternion Wave.

Consider Quaternion Energy W = -vh/r + cP = [-vh/r, cP] the wave equations is

the Second Derivative or Curvature:

X2W = [d/dr, Del]2 [-vh/r, cP] = [(d2/dr2 - Del2), 2d/dr Del ] [-vh/r, cP]

X2W = [-(d2/dr2 - Del2)vh/r - 2cd/dr Del.P, (d2/dr2 - Del2)cP + 2d/dr( Del -vh/r + cDelxP) ]

The Longitudinal wave is the Scalar Wave (Del.P) and the Transverse Wave (DelxP) is the vector Wave.

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Flavio Mitchell

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2y ago

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