What's the general equation related with the "vibrating circular membrane" problem, related with Bessel function of the first kind, that I can just put the "n" order number and the "m"-th positive zero, like J(0,1), that gives me, in this case, as result, the zero of function, resulting in 2.405?
2026-04-02 17:12:31.1775149951
General equation related with the "vibrating circular membrane" problem, related with Bessel function of the first kind
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If you're asking about the wave equation for the problem, it's $\nabla^2 z = \frac{1}{v^2}\frac{\partial^2 z}{\partial t^2}$. If you're asking about the solution that involves Bessel function of the first kind, it's $z = J_n (\frac{k_{mn}r}{a}) \cos (n \theta) \cos (\frac{k_{mn}vt}{a})$, where $k$ is the $m^{th}$ zero of $J_n$