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Eq. 9.20: f(z,t)~ = integral [-inf, inf] A~(k)e^i(kz-wt) dk

where ~ denotes the complex conjugate

the wave equation: f''(z) = (1/v^2) f''(t)

I'm a little confused on how I can separate the variables. Can I assume that I can represent f(z,t) as A sin(kz)cos(kvt) and then calculate the aforementioned 2nd derivatives.

I think my reasoning is correct but my math.... well my math isn't up to par.