# Questions tagged [wave-equation]

For questions related to solutions and analysis of the wave equation.

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### Does the Wave Equation (and other PDEs) define an ODE if I took the behavior in 1D of just one point in space? How I find the ODE from the PDE eqn.?

Does the Wave Equation (and other PDEs) define an ODE if I took the behavior in 1D of just one point in space? How I find the ODE from the PDE eqn.? Intro______________ Since is a conceptual question,...
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### Finding volume element in a wave function

Im working on wave function. I dont know how to find this volume element from the figure eventhough some explanation for factors under the figure . Any help? [ In that paper, the author used $(s,t,u)$ ...
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### Domain of dependence for wave equation on bounded domain

Consider a wave equation, say in $1+1$ dimensions for $\phi(x,t)$, on a bounded domain, say $x \in (0,L)$ and $t \in \mathbb{R}$, with initial values $\phi(x,0)=u(x)$ and $\partial_t \phi(x,0)=v(x)$ ...
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### How to find a PDE satisfying $\rho_{tt}=c^2(\rho_{rr}+2r^{-1}\rho_r)$ with $R=r\rho$?

I'm working on a course problem, In a compressible and uniform fluid the equilibrium density and pressure are $\rho_0$ and $p_0$, respectively. Due to the passage of a compressible perturbation, ...
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### Understanding the boundary condition of spherical waves in the flat spacetime

I am trying to understand one of the two boundary conditions one has to impose to find the solutions of the wave equation in the flat space-time inside a collapsing null shell. For the spherical wave, ...
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### Intuitive explanation of initial condition for wave equation

I've just started a course in Fourier analysis, and have some problem understanding the initial condition of wave equation, and would appreciate if someone would like to explain to me in the easiest ...
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### 1D Wave Equation with Coupled IC's and Non-Homogeneous BC's

Consider the following wave equation: \begin{align} &u_{tt} = u_{xx}, \\\\ &u(x,0) = \frac{1}{2 + \sin x} =: \psi(x), \\\\ &u_t(x,0) = -\frac{\cos x}{(2 + \sin x)^2} = \psi'(x), \\\\ &...
A string is at rest and in a rectilinear form when at $t=0$ begins to be subjected to a constant force distribution perpendicularly from above and along the entire string. This force distribution ...