Waves in Fluids: Basic Properties and Equations

This lecture discusses the fundamental properties of waves in fluids, focusing on surface waves and their mathematical descriptions. The instructor begins by introducing the wave equation and its derivation in various contexts, including sound waves and electromagnetic waves. The discussion emphasizes the behavior of waves in incompressible liquids, highlighting the significance of surface tension and the complexities involved in modeling these phenomena. The instructor illustrates how to derive the wave equation for surface waves, considering small amplitude approximations and the effects of pressure differences. The lecture also covers the physical interpretation of wave propagation, including energy transfer and the relationship between wave speed and fluid properties. Throughout the lecture, examples such as tsunamis are used to contextualize the theoretical concepts. The instructor concludes by addressing questions and summarizing the key points related to wave behavior in different media, setting the stage for further exploration of wave dynamics in subsequent sessions.