Solutions to the classical scalar wave equation in the Godel universe are constructed and their properties investigated. The solutions can be expressed in closed form in terms of exponential and associated Laguerre functions. The frequency spectrum of the perturbations is bounded from below by twice the rotation frequency of the universe, and, for fixed wave number in a certain spatial direction, it is also quantized. The scalar perturbations are compared to the electromagnetic perturbations studied by Mashhoon, and an attempt is made to geometrically interpret the frequency quantization.