FIGURE EX21.2 is a snapshot graph at t=0 s of two waves...

FIGURE EX21.2 is a snapshot graph at $t=0$ s of two waves approaching each other at $1.0 \mathrm{m} / \mathrm{s}$. Draw six snapshot graphs, stacked vertically, showing the string at 1 s intervals from $t=1 \mathrm{s}$ to $t=6 \mathrm{s}$
(FIGURE CAN'T COPY)

Key Concepts

Time Evolution of a Wave

Time evolution of a wave describes how a wave's position and shape change over time. It is crucial for understanding dynamic systems and involves tracking the phase and displacement variables at successive time intervals to analyze the behavior of waves as they travel along a medium.

Superposition Principle

The superposition principle states that when two or more waves meet, the resulting displacement at any point is the algebraic sum of the displacements due to each wave. This principle is central to understanding interference patterns and the combined effects of multiple wave phenomena on a medium.

Wave Propagation

Wave propagation refers to the way disturbances travel through a medium. It involves understanding how the shape of the wave moves with time while maintaining its form, and how its speed determines the translation of the wave profile over a spatial region.

Snapshot Graph Representation

Snapshot graphs are illustrations of the wave's displacement at a specific moment in time. They are used to visualize the wave's profile along the medium at different time intervals, helping to study the evolution and movement of the wave as it propagates.

Transcript

00:01 Now, unfortunately, i went through this whole thing and didn't upload properly.

00:08 So i'm going to go through this verbally.

00:11 What i did is i wrote one second here, t equals one.

00:18 And all i did is i moved the red wave to the right one and the green wave to the left one.

00:27 That put them both at five, and so the wave would look like this.

00:33 The combined wave will look like that, the superimposed wave.

00:41 T equals two, all we have to do is continue to move the red one one meter to the right and the green one one meter to the left.

00:51 So that's what i've drawn down here.

00:54 The red one starts at two and ends at six.

00:57 The green one now starts at four, and ends at eight.

01:05 But what you can see here is that right here in the middle, you've got one -half, i guess i should use black for this, maybe, one -half plus negative one -half, because we're adding the two together.

01:22 The red wave is at one -half, and the green wave is at negative one -half.

01:27 One -half plus negative one -half is zero, and that's why i have a zero.

01:32 Right in between, right here.

01:39 And so when we add the red one to the green one, we get the blue one.

01:49 T equals three.

01:50 So when we move the red wave to the right, it's not going to extend from three to seven.

01:59 If we move the green wave to the left, it is also going to extend from three to seven...