Chapter18-S09 - Chapter 18 Superposition and Standing Waves...

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Chapter 18 Superposition and Standing Waves 18.1 Superposition and Interference Superposition principle: If two or more traveling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of the individual waves. Two traveling waves can pass through each other without being destroyed or even altered. When two waves combine in space, they interfere to produce a resultant wave. The interference may be constructive (when the individual displacements are in the same direction) or destructive (when the
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Superposition of Sinusoidal Waves Let us apply the superposition principle to two sinusoidal waves which are traveling to the same direction and have the same frequency, wavelength, and amplitude but different in phase : The resultant wave function y also is sinusoidal and has the same frequency and wavelength as the individual waves. The amplitude of the resultant wave is 2Acos( φ /2), ( 29 ( 29 ( 29 ( 29 [ ] + - = + - = + + - + - = + - + - = + = 2 sin 2 cos 2 2 sin 2 cos 2 sin sin sin sin sin sin 2 1 φ ϖ t kx A y b a b a b a t kx t kx A t kx A t kx A y y y k
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cos( φ /2) = ±1 when
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Chapter18-S09 - Chapter 18 Superposition and Standing Waves...

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