W5

Superposition (Ch. 17)

Lectures

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

• Tuesday (pdf before annotation, pdf after annotation)

• Thursday (pdf before annotation, pdf after annotation); Colorado PhETs

Example Videos

From TA Ian Chaffey.

• Ex. 17.42

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

• When waves overlap, the resulting displacement is the sum of each displacement

• Standing waves only "move in place."

• Standing waves can be understood as the sum of traveling waves

• Use trig identities for the sum of sines to derive properties of the overlapping waves

• Music: explain how guitars, flutes, and clarinets work in terms of standing waves

• Interference: explain how noise-cancelling headphones work in terms of standing waves

Things to think about

• The book very notably avoids talking about energy. What happens to the energy of a wave when it interferes?

Reading Guide

• Do not get caught up in the trigonometric identities used in this chapter! They show how to derive ideas, but the derivations are not the point! All of the trig identities are ways of simplifying sums of sines.

• It may help to focus on concrete applications of these ideas: string instruments, wind instruments, and noise-cancelling headphones. The ideas are more general than that, but it helps to have a specific example in mind.

• The key applications are sections 17.3 (strings) and 17.4 (wind instruments).

• You may skip (or just skim) section 17.7 about interference in 2D and 3D. It's slightly more complicated, but doesn't introduce any new physics. This is not a class about trigonometry.

• Sections 17.5, 17.6, and 17.8 talk about interference. Don't get caught up in the math: focus on what's happening when you have noise-cancelling head phones. There are no new ideas, just consequences of superposition.

• By the way: this chapter really calls for animations. I strongly encourage you to check out the videos under "neat links" at the bottom of the page.

Animated version of Fig. 17.4: the red and green waves are moving in opposite directions (dots highlight the crest of each wave). The dark blue line is the sum of the two waves.