- #1

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The result is immediate and correct.

However what I don't understand is why k has to be negative. Shouldn't [tex] \frac{g^{''}(t)}{g(t)} [/tex] and [tex] \frac{f^{''}(x)}{f(x)} [/tex] be any non-zero number since the change of displacement in oscillation can be either positive or negative? That said, shouldn't the wave equation give also formulas of hyperbolic sines and cosines for specific parts of the oscillation?

P.S. I am most interested in deriving the E/M sine wave formulas:

[tex] E=E_{max}cos(kx - ωt + φ_{0}) [/tex] or [tex] E=E_{max}cos(kx + ωt + φ_{0}) [/tex]

[tex] B=B_{max}cos(kx - ωt + φ_{0}) [/tex] or [tex] B=B_{max}cos(kx + ωt + φ_{0}) [/tex]

Thank you very much!!