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viewnote15 - PHYS 302 Unit 15 Viewing Notes Athabasca...

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PHYS 302 : Unit 15 Viewing Notes – Athabasca University 1 PHYS 302: Vibrations and Waves – Unit 15 Viewing Notes Please ignore the reference to boundary conditions of electromagnetic waves (as having been discussed in the previous lecture). We will apply boundary conditions as needed. Previously we discussed one-dimensional propagation of waves along a string or comparable long object. While we discussed normal modes in dimensions higher than one, we have not yet done so in the context of waves. As with normal modes, the transition from one dimension to three dimensions is straightforward, as reflected in the first equations of the lecture. The scalar wavenumber becomes a wave vector, represented in terms of its components along the unit vectors for directions ˆ ˆ ˆ ( , , ) x y z . In three dimensions, the wave vector is in the direction of propagation of the wave: ˆ ˆ ˆ x y z k k x k y k z (2:00). It does not make sense to define the wavelength λ by a vector, but its scalar value remains 2 k , with k being the magnitude of the wave vector (and still called the wavenumber), that is, 2 2 2 x y z k k k k k . The speed of propagation for light in a vacuum (nondispersive) is c . In the phase velocity equation k v , this allows for writing the frequency as k : ω =kc (2:40). We briefly discussed polarization in earlier units, and polarization is important for electromagnetic (EM) radiation. Remember that polarization is a type of ordering. EM radiation can be polarized, and the direction of polarization indicates the direction of the electric field in the radiation. For example, radio waves from an antenna are usually highly polarized in a direction that relates to the geometry of the antenna. Microwaves are often similarly polarized by the small antenna or emitting structure that makes the waves. Light that we see in our daily lives is typically not highly polarized, but special types of light, like that from lasers, are polarized. The lecture also refers to radar waves, which are polarized. For propagation of EM waves between two plates (discussed in the lecture), the waves (and the wave vector) propagate in the z direction, and the polarization, or direction of the electric field in the EM wave, is in the y direction. These are, respectively, the horizontal and vertical directions, and the plates are considered large (with respect to wavelength) in these directions. The reason why the electric field rather than the magnetic field (which can be shown to be at right angles to the electric field) specifies the polarization of an EM wave is that electric fields move charges around. In fact, an electric field E is defined as the force on a unit charge, so that for a charge q , F q E , where F is the force on the charge. Thus, applying an electric field to charges makes them feel a force and accelerate.
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