Waves

The wave is a physical phenomenon that is found in a variety of contexts, a perturbation in the medium. You undoubtedly know about ocean waves and have probably played with a stretched slinky toy, producing undulations which move rapidly along the slinky. Other examples of waves are sound, vibrations in solids, and light (photons have the particularity of sharing characteristics of both waves and particles).

Despite the vast differences in these different types of waves, they all consist of a fluctuation around an equilibrium position caused by a restoring force, and can be described by the same types of mathematical equations. Understanding these equations is a powerful tool because it will let you understand the basics of a wide variety of seemingly unrelated phenomena. The purpose of this section is to describe the kinematics of waves, i.e., to provide tools for describing the form and motion of all waves irrespective of their underlying physical mechanisms.

In this chapter we learn first about the basic properties of waves and introduce the most common type of wave, called the sinusoidal (sine) wave. In fact just about any type of wave can be expressed as a combination of sine functions using a technique proposed by Joseph Fourier. Examples of waves seen in the real world are presented. We then learn about the superposition principle, which allows us to construct complex wave patterns by superimposing sine waves. Using these ideas, we discuss the related ideas of beats and interferometry. Finally, the ideas of wave packets and group velocity are introduced.

Waves in one dimension

1. The Mathematics of Waves
2. Transverse, Longitudinal, and Torsional waves
3. Sine Waves
4. Types of Waves
5. Sound Waves
6. Light
7. Superposition Principle
8. Beats
9. Interferometers
10. Thin Films
11. Derivatives
12. Fourier Transforms
13. Group Velocity

Examples

Problems

Solutions

Terminology

Waves in two and three dimensions

1. Introduction
2. Math:Vectors
3. Plane Waves
4. Superposition of Plane Waves
5. Single slit Diffraction
6. Double slit Diffraction
7. Diffraction Grating

Problems

Geometrical optics

1. Introduction
2. Reflection and Refraction
3. Total Internal Reflection
4. Anisotropic Media
5. Optical Instruments
6. Fermat's Principle

Problems