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This course has two complementary goals.
The first is to provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. This will allow you to gain a deeper appreciation for the true nature and beauty of phenomena like music and rainbows, which all of us observe or experience every day.
The second goal is
to provide you with the skill of using a broad range of techniques that can greatly simplify the analysis and solution of complex systems. These techniques include complex numbers, combinations of oscillatory and exponentially decaying functions, resonance, normal modes, Cramer's rule for solving several equations in several variables, boundary conditions, general wave equations, Fourier decomposition, dispersive and non-dispersive media, phase and group velocities, sound cavities and wave guides, polarization, Doppler effect, reflection and refraction, Fresnel's equation for transmission and reflection, total internal reflection, constructive and destructive interference, and diffraction.
Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string. In fact, without vibrations and waves, we could not recognize the universe around us at all!
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