ABSTRACT
We will study the vibrations of strings and other media, and present related topics from the science of acoustics. The case of vibration of a string has been mentioned in §17.3 and an example presented in §17.6.1. Vibrations are defined by hyperbolic equations which are extensively discussed in Chapters 17, 18, and 19. The propagation and dispersion of waves has also been mentioned in previous chapters. We will study some aspects of vibrating membranes and acoustics as to how they are related to conformal mapping. In engineering studies the notation w = u + iv has been used for transverse deflections. However, since we use w for the model plane (w-plane) in conformal mappings, we will, therefore, use ϕ for the potential function to represent deflection.
