Waves in Fluids: Basic Properties and Equations

This lecture discusses the fundamental properties of waves in fluids, focusing on surface waves in incompressible liquids. The instructor begins by reviewing the wave equation and its derivation, emphasizing its application to various scenarios, including sound waves and electromagnetic waves. The lecture highlights the complexities of surface waves, which are influenced by atmospheric pressure, water pressure, and surface tension. The instructor explains how these waves differ from longitudinal and transverse waves, illustrating the behavior of water molecules under wave influence. The discussion progresses to the mathematical representation of wave motion, including the derivation of the wave equation in three dimensions. The instructor also explores the implications of wave propagation speed and the relationship between wave properties and physical parameters. Throughout the lecture, practical examples and visual demonstrations are used to enhance understanding, culminating in a discussion of energy density in wave motion and its significance in various physical contexts.