Rectangular membrane normal mode
= Rectangular membrane normal mode
{title2=$f_{pq}=\frac c2\sqrt{p^2/a^2+q^2/b^2}$}
For a rectangle of sides a and b with fixed edges, <separation of variables> gives $\psi=A\sin(p\pi x/a)\sin(q\pi y/b)\cos(\omega t+\phi)$ with positive integers p and q. Its <angular frequency> is $\omega=c\pi\sqrt{p^2/a^2+q^2/b^2}$. Zero integers produce the trivial displacement, not a lower <mode>. The p−1 and q−1 interior nodal lines divide alternating-sign lobes.