Perturbations of black holes (Schwarzschild, Reissner-Nordstrom and Kerr) can be treated by simple radial wave equations. It is shown that the massless scalar radial equation is a form of the spin-weighted spheroidal wave equation. The region in r corresponding to the usual angular argument (cos$\theta$, $\theta$ real) for such functions is the black hole interior, $r\in(r_-,r_+)$ where $r_-,r_+$ are the inner and outer horizon radii respectively. We restrict ourselves to axisymmetric scalar waves. (Because of the spherical symmetry this is no restriction in the Schwarzschild and Reissner-Nordstrom backgrounds, but it is a physical restriction in the Kerr background.) In these cases the spin-weighted spheroidal harmonics correspond to imaginary-frequency waves, i.e. to exponentially growing or decaying waves that fall inward across the outer horizon r$_+$ and are converted to waves moving in the opposite direction as they cross the r$_-$-horizon (r is a timelike coordinate when $r\in(r_-,r_+)$). These modes are exactly analogous to the external quasi-normal modes of the black hole. There is always one zero-frequency mode, and l non-zero imaginary-frequency modes. Here l is the angular momentum eigen-number associated with the angular decomposition.