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waveinter

waveinter - Wave Interference with Applications Math Aside...

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Wave Interference with Applications Math Aside : The following trigonometry identity will be useful for this topic: sin α + sin β = 2cos[( α - β )/2] sin[( α + β )/2] The superposition principle shows how to find the wave function when more than one wave occupies a string. We call this wave interference, wave addition or wave superposition; these all mean simply, add the waves, y = y 1 + y 2 . Applications One result of this principle is the phenomenon of constructive and destructive interference . We will also examine two more applications: standing waves and beats .

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I. Adding two identical sinusoidal traveling waves differing only by a phase constant, δ A. One dimension Using the trig. identity and superposition principle above, y = A sin(kx - ϖ t) + A sin(kx - ϖ t + δ ) y = 2A cos[ δ /2] sin[kx - ϖ t + δ /2] Special cases: δ = 0 constructive interference Corresponding points line up, i.e. crests line up with crests, and troughs line up with troughs.
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waveinter - Wave Interference with Applications Math Aside...

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