Wave Propagation in 1-D Spiral geometry
  In this article, we investigate the wave equation in spiral geometry and study the modes of vibrations of a one-dimensional (1-D) string in spiral shape. Here we show that the problem of wave propagation along a spiral can be reduced to Bessel differential equation and hence, very closely related to the problem of radial waves of two-dimensional (2-D) vibrating membrane in circular geometry. 
Deep Chatterjee and Rajesh K. Nayak
physics.class-ph