This is the fourth in a series of four volumes, all written at an elementary calculus level. The complete course covers the most important areas of classical physics, such as mechanics, thermodynamics, statistical mechanics, electromagnetism, waves, and optics. The volumes are the result of a translation, an in-depth revision and an update of the Italian version published by Decibel-Zanichelli. This fourth volume deals with oscillations, waves, and light.
It is assumed that the reader knows differential calculus and the simplest properties of the vector fields (the same as in Volume 3), such as the gradient of a scalar field, the divergence and curl of a vector field, and the basic theorems on the line integral of a gradient, the Gauss divergence theorem and the Stokes curl theorem. We shall also assume that the reader has already learned the basic concepts of mechanics and electromagnetism up to Maxwell’s equations, as developed in the first volumes of this course, to which we shall make explicit reference when needed, or equivalent ones.
Oscillations about a stable state of equilibrium are a very common natural phenomenon, present in all sectors of physics ranging from mechanics to electromagnetism and from astrophysics to atomic and nuclear physics. A spider hanging from its gossamer thread, if displaced from the equilibrium position, oscillates back and forth as long as passive resistances do not stop it. A blade of grass pushed by the wind moves periodically up and down. A boat on the surface of a lake oscillates under the action of the waves. Large systems vibrate as well. The earth’s atmosphere does so under the periodic action of the moon over a period of about 12 h. The earth itself vibrates for a while when hit by an intense seismic shock, as do extremely small objects. Light itself is produced by the vibrations of atoms, namely the oscillations of the electrons they contain, which, as all accelerating charges do, produce an electromagnetic wave. An electric circuit containing an inductance and a capacitance performs harmonic, electric oscillations that are completely similar to the mechanical oscillations of a pendulum. Electric and the magnetic fields also oscillate in a vacuum, when they are the fields of an electromagnetic wave. And space-time itself vibrates when a gravitational wave crosses it.
1. Oscillations of Systems with One Degree of Freedom
2. Oscillations of Systems with Several Degrees of Freedom
5. Diffraction, Interference, Coherence
7. Optical Images
8. Images and Diffraction
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