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- Wave equation (4)
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Articles 31 - 36 of 36
Full-Text Articles in Physics
References And Suggestions For Further Reading (Appendix C), Charles G. Torre
References And Suggestions For Further Reading (Appendix C), Charles G. Torre
Foundations of Wave Phenomena
References and Suggestions for Further Reading (Appendix C)
Problem Set 9, Charles G. Torre
14 Conservation Of Energy, Charles G. Torre
14 Conservation Of Energy, Charles G. Torre
Foundations of Wave Phenomena
After all of these developments it is nice to keep in mind the idea that the wave equation describes (a continuum limit of) a network of coupled oscillators. This raises an interesting question. Certainly you have seen by now how important energy and momentum — and their conservation — are for understanding the behavior of dynamical systems such as an oscillator. If a wave is essentially the collective motion of many oscillators, might not there be a notion of conserved energy and momentum for waves? If you’ve ever been to the beach and swam in the ocean you know that …
13 Spherical Coordinates, Charles G. Torre
13 Spherical Coordinates, Charles G. Torre
Foundations of Wave Phenomena
The spherical coordinates of a point p can be obtained by the following geometric construction. The value of r represents the distance from the point p to the origin (which you can put wherever you like). The value of ✓ is the angle between the positive z-axis and a line l drawn from the origin to p. The value of " is the angle made with the x-axis by the projection of l into the x-y plane (z = 0). Note: for points in the x-y plane, r and " (not ✓) are polar coordinates. The coordinates (r, ✓, ") …
09 The Wave Equation In 3 Dimensions, Charles G. Torre
09 The Wave Equation In 3 Dimensions, Charles G. Torre
Foundations of Wave Phenomena
We now turn to the 3-dimensional version of the wave equation, which can be used to describe a variety of wavelike phenomena, e.g., sound waves and electromagnetic waves. One could derive this version of the wave equation much as we did the one-dimensional version by generalizing our line of coupled oscillators to a 3-dimensional array of oscillators. For many purposes, e.g., modeling propagation of sound, this provides a useful discrete model of a three dimensional solid.
Problem Set 4, Charles G. Torre