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Introduction to the Physics of Waves by Tim Freegarde

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15

Waves in three dimensions

15.1 Waves in multiple dimensions

Our treatment of wave propagation so far has mostly been restricted to geometries that are essentially one-dimensional: absolutely, as with transverse waves on a string; approximately, as in the longitudinal waves of a narrow column of air; or implicitly, as for the propagation of periodic plane waves in three-dimensional space. We have, it is true, shown the spreading of waves (through diffraction, or simply because they emanate from a point), which implies the presence of and dependence upon additional spatial dimensions; and in our examination of ocean waves, the Huygens method of wavefront construction and its application to diffraction, we have more explicitly allowed at ...

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