Classical (I.e. not Quantum) Waves
Find speed of wave on a string, which is flexible and not displaced much
The mass of a segment of a string with mass per unit length ? is
Another calculation, with the kink, is instructive:
There is an unbalanced force on the kink. The right hand end has no y component force, the left end has a force
Reflections at the end:
Traveling Waves-start with Harmonic Waves, exciting with a simple harmonic motion of frequency f, wavelength ? = v/f
Sometimes we want the choice of the origin of x and t to be arbitrary, so we have to throw in an “initial phase” ?
Review of Simple Harmonic Motion
SHM formula application to wave:
String fixed at 0 and L: Standing Waves
Some trig: what if we have two traveling waves going in opposite directions:
What if we add (traveling) waves with different wave lengths?
Wave Equation on String, generalize our analysis of kink:
Or, canceling the dx
Solutions of the Wave Equation 1. Traveling Wave solutions
2. The “Normal Modes” of the string with fixed ends:
This is the familiar SHO equation, with solutions
Special Problem, preparation for Test, Due Monday 18 October, questions answered 13,15 Oct.
Email: willis@nevis1.columbia.edu
Home Page: www.nevis.columbia.edu/~willis
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