- #1
pt176900
- 27
- 0
From Griffiths: Problem 9.4 Obtain Eq. 9.20 directly from the wave equation, by separation of variables.
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.
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.