chp38_10 - PHY2061 R. D. Field The Wave Equation 2 y( x, t...

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PHY2061 R. D. Field Department of Physics chp38_10.doc University of Florida The Wave Equation 2 22 2 2 1 0 yxt xv t (, ) ) −= Whenever analysis of a system results in an equation of the form given above then we know that the system supports traveling waves propagating at speed v. General Proof: If y = y(x,t) = f(x-vt) then y x f y x f y t vf y t = = ′′ =− = ′′ 2 2 2 2 2 and 2 2 2 1 0 t ff ) ) ′′ − ′′ = . Proof for Harmonic Wave:
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