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By explict differentiation, check that the functions f1, f2 below satisfy the wave equation.
Shwo that f4 does not.
f1(z, t) = Ae^(-b(z-vt)^2)

f2(z, t) = Asin[b(z -vt)]

f4(z, t) = Ae^(-b(bz^2 + vt))

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By explict differentiation, it shows that two functions satisfty the wave equation.

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Then using the product and chain rules,
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