Question
By explicit differentiation, check that the functions $f_{1}, f_{2},$ and $f_{3}$ in the text satisfy the wave equation. Show that $f_{4}$ and $f_{5}$ do not.
Step 1
Step 1: The wave equation is given by $\frac{\partial^2 f}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 f}{\partial t^2}$, where $v$ is the speed of propagation. Show more…
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Show by differentiation and substitution that any function of the form $y=f(x \pm v t)$ satisfies the wave equation (Equation 14.5 ).
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PARTIAL DIFFERENTIAL EQUATIONS
Introduction
Show by differentiation and substitution that $a n y$ function of the form $y=f(x \pm v t)$ satisfies the wave equation (Equation 14.5 ).
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