To aid comprehension of cochlear traveling waves, the present article will explain this complex phenomenon in terms of its underlying principles: (1) fluid mechanics, with particular reference to a tangible, analogous event, wave transformation on sloping beaches; (2) the central role of the cochlear stiffness gradient with respect to an energy exchange between travel speed and amplitude of cochlear waves, low pass filter action with distance, and impedance matching for the benefit of wave progression; (3) spatial domain and frequency domain considerations; (4) the solution to the classic dilemma between cochlear tuning and damping; and (5) the task of the helicotrema. I will not discuss the ultimate mechanical stimulation of cochlear hair cells that is mediated by shearing interactions between the tectorial membrane and the organ proper.