6B Ch 15 (Official)

# Fourier s theorem any complex periodic wave can be

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Unformatted text preview: The displacement at any point is the vector sum of the displacements of all waves passing through that point at that instant. Fourier s theorem: Any complex periodic wave can be written as the sum of sinusoidal waves of different amplitudes, frequencies, and phases. t=0 D1 = A D3 = 1/5A cos cos kx D2 = -1/3A cos 3kx 5kx A= k= x= Superposition of Sinusoidal Waves • Assume two waves are traveling in the same direction, with the same frequency, wavelength and amplitude • The waves differ in phase • y1 = A sin (kx - t) • y2 = A sin (kx - t + ) • y = y1+y2 = 2A cos ( /2) sin (kx - t + /2) A sinusoidal wave! Sinusoidal Waves with Constructive Interference • When = 0, then cos ( /2) = 1 • The amplitude of the resultant wave is 2A – The crests of one wave coincide with the crests of the other wave • The waves interfere constructively Sinusoidal Waves with Destructive Interference • When = , then cos ( /2) = 0 – Also any odd multiple of • The amplitude of the resultant wave is 0 – Crests of one wave coincides with troughs of the other wave • The waves interfere destructively Sinusoid...
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## This document was uploaded on 02/21/2014 for the course CHEM 110A 110a at UCLA.

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