Warm-Up Exercise 21

Due 12:15 pm, Mon 15 Oct 2012

Physics 123, Fall 2012

Reading assignment: PpP 4.1,5.1

PpP states that "a pure sine wave has a precisely defined frequency... but a completely undefined position." What does it mean to have a "completely undefined position"?

If you plot a wave function like y=sin(x), the wave exists from x = -infinity to x = +infinity. Therefore there is not a region of space where you can say "The wave is here", or "The wave is not here".

PpP states that "the 'envelope' of the wave... can travel at a different speed than the ripples inside of the envelope." That was a very hard concept for me to grasp when I was a student, but fortunately computer animation has come a long way since then. Browse to http://en.wikipedia.org/wiki/Group_velocity, and look at the first two figures of the page. (I actually created the second figure myself.) Observe that the envelope and the ripples are indeed traveling at different speeds! For each figure, measure the speed of travel on your monitor (cm/s) for both the envelope and the ripples.

Your results will depend on size of monitor and/or zoom level. But the ratio of envelope to ripple speed should be the same as me. My results were: * Top Fig: speed of envelope (green dots) = 0.46 cm/s, speed of ripples (red dot) = 0.92 cm/s * Second Fig: speed of envelope = 1.50 cm/s; speed of ripples = -0.54 (note the negative sign!)

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