W4

Wave (Ch. 16)

Last week we learned that simple harmonic motion is a generic feature of a system near equilibrium. When you connect a bunch of harmonic oscillators together, you get waves.

The solution for simple harmonic motion is a function of time, x(t). The solution for a wave is a function of position and time, D(x,t).

Waves transmit energy from one place to another in a medium.

Please see the reading guide below. Please focus on Section 16.3: it presents "the solution." On the other hand, Sections 16.4 and 16.6 are "advanced topics" in multivariable calculus. I encourage you to read them to see the derivation of the wave equation, but you won't be responsible for the material.

Lectures

Additional lectures (from Spring 2020) are linked at the bottom of the page.

• Tue: Lecture (pdf)

• Thu: Lecture (pre-lecture pdf, pdf)

Example Videos

From TA Ian Chaffey.

• Ex. 16.60

• Ex. 16.82

Reminder: TA office hours are on Friday at 1pm, please find the link pinned to the #general channel of our Slack.

Learning Objectives This Week

• See how a wave is a collective motion of many simple harmonic oscillators making up a medium.

• Understand the properties of a wave solution: amplitude, (angular) frequency/period, wave number, phase.

• Identify the ways in which transverse and longitudinal waves are the same and different.

• See how the wave equation comes from F=ma applied to the microphysics of a medium (Sec 16.4 and 16.6).

• Understand the energy in a wave in one, two, and three dimensions.

Reading Guide

• 16.1: skim this introductory section; the most important result here is the expression for the wave speed, (16.1).

• 16.2: You can skim this section. All that matters is that a wave is described by a displacement, D(x,t), which is a function of both position and time. Ignore all the weird nomenclature: snapshot graph, history graph, leading/trailing edge.

• 16.3: Focus on this section. This is the core of the chapter. In particular:

• Equation (16.6): wavelength is the ratio of a property of the medium to a property of the source

• Equation (16.8): the displacement is a function of a single combination of two variables: x-vt. Be sure that you appreciate the significance of the minus sign.

• The idea of a wave number is presented in (16.11); think of it as an angular frequency in space.

• Make sure you understand Figure 16.16: the "wave" is a collective phenomenon that moves in the x direction. However, each piece of the wave (some fixed x) moves up and down in the perpendicular direction.

• 16.4: this is an "advanced topic," you're not responsible for reproducing the steps in this chapter, but please read it. It shows how Newton's laws produce the wave equation, (16.28).

• 16.5: this section is a qualitative discussion of some examples of wave phenomena: sound and light. We will skip the index of refraction.

• 16.6: another "advanced topic," you don't have to reproduce the steps, but please read it. It re-does 16.4 for longitudinal waves.. The result is equation (16.50), which is the exact same form as equation (16.28).

• 16.7 and 16.8: 2D and 3D waves. Pay attention to the discussion of phase and phase difference. Section 16.8 is basically "energy and waves." The main idea is the definition of intensity and how it scales with distance. Make sure you follow the first half of this section. We won't dig too much into decibels, but you should read this section (it may show up in your explainer problem).

• 16.9: We will not go over the Doppler effect in this class. It's a neat topic, though, and I encourage you to look it over. Some of the ideas will be helpful (but not necessary) for next week.