Introducing Waves: Strings and Springs
Michael Fowler 3/28/06
One-Dimensional Traveling Waves
The most important kinds of traveling waves in everyday life are electromagnetic waves, sound
waves, and perhaps water waves, depending on where you live.
(Electromagnetic waves include
X-rays, light, heat, microwaves, radio, etc.)
But it’s tough to analyze waves spreading out in
three dimensions, reflecting off objects, etc., so we begin with the simplest interesting examples
of waves, those restricted to move along a line.
Let’s start with a rope, like a clothesline, stretched between two hooks.
You take one end off the
hook, holding the rope, and, keeping it stretched fairly tight, wave your hand up and back once.
If you do it fast enough, you’ll see a single bump travel along the rope:
wave moving this way
This is the simplest example of a
You can make waves of different shapes by
moving your hand up and down in different patterns, for example an upward bump followed by a
dip, or two bumps.
You’ll find that the traveling wave
keeps the same shape
as it moves down
the rope. (That’s before it reaches the end, of course—things get more complicated at that