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5. Consider the following candidate one dimensional wave functions: f = A(x³ - 3vtx² +3v²t²x-v³t³) • f = Ax + B(vt)³ where A and B are constants f = A(x+vt) (x - vt) where A is a constant f = A sin (z/L) cos (vt/L) where A and I are constants a) First, using the wave equation, determine which of the following functions could represent waves. b) Any function that solves the one-dimensional wave equation should depend functionally on the combination xtvt. For the functions from part a) that solve the wave equation, show that they can indeed be written in this form.

5. Consider the following candidate one dimensional wave functions: f = A(x³ - 3vtx² +3v²t²x-v³t³) • f = Ax + B(vt)³ where A and B are constants f = A(x+vt) (x - vt) where A is a constant f = A sin (z/L) cos (vt/L) where A and I are constants a) First, using the wave equation, determine which of the following functions could represent waves. b) Any function that solves the one-dimensional wave equation should depend functionally on the combination xtvt. For the functions from part a) that solve the wave equation, show that they can indeed be written in this form.

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5. Consider the following candidate one dimensional wave functions: f = A(x³ - 3vtx² +3v²t²x-v³t³) • f = Ax + B(vt)³ where A and B are constants f = A(x+vt) (x - vt) where A is a constant f = A sin (z/L) cos (vt/L) where A and I are constants a) First, using the wave equation, determine which of the following functions could represent waves. b) Any function that solves the one-dimensional wave equation should depend functionally on the combination xtvt. For the functions from part a) that solve the wave equation, show that they can indeed be written in this form.
Transcribed Image Text:5. Consider the following candidate one dimensional wave functions: f = A(x³ - 3vtx² +3v²t²x-v³t³) • f = Ax + B(vt)³ where A and B are constants f = A(x+vt) (x - vt) where A is a constant f = A sin (z/L) cos (vt/L) where A and I are constants a) First, using the wave equation, determine which of the following functions could represent waves. b) Any function that solves the one-dimensional wave equation should depend functionally on the combination xtvt. For the functions from part a) that solve the wave equation, show that they can indeed be written in this form.
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