This week is all about developing some language around the concept of waves and starting to notice the behavior of waves in the world. Over the next several weeks we will explore an whole range of phenomena that arise because of the underlying features and behavior of waves which is why it is so important to make sense of this week.

We will start with a simple and classic demonstration of the propagation of a pulse along a spring/string. Think about how you might argue that springs and strings are really just different forms of very similar systems. Be aware as you watch this clip that Walt has just finished talking about the periodic behavior of a series of masses strung like beads along an elastic string which he refers to as coupled oscillators. Perhaps you will be comfortable thinking of a string or spring as just a bunch of very small beads very close together -- how calculus of you!

Pulse Propagation: (3 min)

If you watch the full video from lecture 7 you will note that Walt now spends 20 min developing the differential equation for this pulse on a string. What I am most interested in is your ability to understand what this differential equation is telling you about it's solution. This next clip moves rapidly through some very important ideas and it will be valuable for you to work through it almost 1 statement at a time to be sure you understand why his statements are actually correct.

Wave Equation Thinking: (3 min)

Of particular interest is his discussion about the units of C and the eventual statement that it is the velocity. The expression he gives for the velocity of a pulse on a string is an important one for you to remember -- the world will expect it of you.

This next small clip is a interesting discussion of how the sign between the x and t terms defines the direction of the wave. Don't oversimplify this -- it is tempting to just think of it as a simple translation along the axis which is partly true but the more important idea is that a particular value of x+vt will turn out to be an angle that labels a particular point on the shape of the pulse.

Propagation Direction: (3.5 min)

These next clips are a nice discussion and argument for why pulses (and by extension waves) reflect differently from rigid end points and loose end points. These, as Walt points out, are usually referred to as closed and open boundary conditions which will be important soon. No need to do more than scan through these ones.

Rigid (closed) End Point: (4.5 min)

Loose (open) End Point: (4.5 min)

Once you have seen this discussion now watch the demonstration of this effect in action. I have the same equipment and I can bring it to class if you think it will give you a different sense but for now please watch and think.

Reflections at open and closed: (5 min)