Physics 302
Vibrations and Waves


Physics 302
Vibrations and Waves

Course Manual


Welcome to Physics 302: Vibrations and Waves. The purpose of this course is to enable you to understand oscillations and wave phenomena in several domains. Much of the course will focus on mechanical waves and systems since the basic laws of mechanics should already be familiar to you. We will discuss general aspects of waves that are common to electromagnetic waves, but will not examine the basic laws allowing electromagnetic waves to exist in classical physics. We will also discuss quantum mechanical waves, again without discussing the fundamental aspects of quantum mechanics underlying a view of the world in which waves are found in unexpected places.

Mechanical Waves

Mechanical waves include a large number of interesting systems, many of them fundamental to our everyday lives. Under mechanical systems, we will include anything that is well described by Newton’s Laws or by simple extensions of them, ranging from pendulums and springs to water waves and sound. Oscillations in electrical systems, which are analogous, interesting, and important, will be addressed at the same time. Although there can be some relationship between oscillations in electrical systems and electromagnetic waves, they are not really the same, so electromagnetic waves will be the next major topic.

Electromagnetic Waves

Electromagnetic waves have light as their most “visible” example. The manifestations of the wave nature of light are subtle: Newton, for example, regarded light as a stream of particles—not as a wave. Many students are first introduced to “wave-particle duality” in discussions of light. The history of wave-particle duality has brought about an artificial division, sometimes emphasizing the wave aspects, and other times emphasizing the particle aspects. Of course, there is no real contradiction: light shows both aspects. Learning how to work with particles (such as in a prerequisite mechanics course) separately from waves (in this course) simply gives us tools to work with limited aspects of light. In addition to light, other types of electromagnetic waves range from radio waves and microwaves (the most wave-like), to X-rays and gamma rays (the most particle-like). A major intellectual development of the twentieth century was the realization that wave-particle duality extends well beyond electromagnetic waves, indeed to “mere” particles. This is one basis of quantum mechanics.

Quantum Mechanical Waves

Quantum mechanical waves allow an understanding of a large part of the subatomic world. Some techniques that you will learn in this course describe the aspects of the wave nature of quantum mechanical waves that are largely shared with other waves. Based on what we know about particles, much of quantum mechanical behaviour seems counterintuitive. In this course, we will try to give enough attention to how waves work that your knowledge of the wave aspects of matter will provide you with a powerful tool kit to later advance your understanding of this subject.


The level of understanding we seek has a mathematical basis. You will need a basic understanding of calculus, mostly differential calculus, to proceed through much of the course. Linear algebra is not a prerequisite, so a small amount of it will be introduced as needed. The mathematics in this course is normally presented at a second- to third-year university level. Its clear presentation gives you a glimpse of what you would study more fully in a course on partial differential equations, in many ways the most basic language of physics.

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