I understand the mathematical origin of complex eigenvalues, and that complex eigenvalues [come in pairs](http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#In_the_complex_domain). But what is the meaning of the imaginary part? In particular I refer to an acoustic problem (Helmholtz equation) coupled with plate vibrations: the eigenvalues represent frequencies, so what's the physical meaning of two eigenvalues with the same real value and opposite imaginary values (conjugated)? What's the meaning of pure imaginary eigenvalues?