Linked Questions

1 vote
1 answer
117 views

How is the wave equation derived or discovered? [duplicate]

I don't really understand where the fundamental or general wave equation $$\frac{\partial^2y}{\partial t^2} = v^2\frac{\partial^2y}{\partial x^2}$$ comes from. I understood the derivation of wave ...
Jack's user avatar
  • 31
16 votes
3 answers
9k views

How to "derive" the wave equation without refering to strings?

The wave equation in $3$ dimensions is simply: $$\nabla^2\psi = \dfrac{1}{v^2} \dfrac{\partial^2}{\partial t^2}\psi,$$ and the intuition behind this is that at each point of space with coordinates $(...
Gold's user avatar
  • 36.4k
12 votes
2 answers
7k views

What should be the intuitive explanation of wave equation?

$$\dfrac {\partial^2 y}{{\partial x}^2} = \dfrac{1}{v^2} \dfrac{\partial^2 y}{{\partial t}^2}$$ is the wave equation in one dimension. But what should be the intuition behind it? That is, what meaning ...
user avatar
6 votes
4 answers
3k views

What are waves? Where does the wave equation come from?

I'm taking a course on waves and optics using Young and Freedman's University Physics, but I'm a bit confused about a couple of things. I've also looked at Griffiths' Introduction to Electrodynamics ...
Danny's user avatar
  • 350
3 votes
5 answers
2k views

Wave Equation derivation

I'm curious about part of the derivation of the wave equation as is done in all references that I've seen so far (I'm gonna reproduce only the part that's puzzling me). We apply Newton's second law ...
julesc's user avatar
  • 43
2 votes
2 answers
597 views

Physical Interpretation of d'Alembert Operator

$$\mathop{{}\Box}\nolimits=\frac{1}{c^2}\frac{\partial^2}{\partial t^2}-\mathop{{}\bigtriangleup}\nolimits$$ is the d'Alembert-operator. It seems to consist of an oscillation and a diffusion. Is there ...
kalle's user avatar
  • 938
1 vote
2 answers
983 views

Deriving speed of waves equation [duplicate]

I am trying to derive the speed of a wave equation $$v = \sqrt{F/\mu}$$ starting from a segment of string under tension with a force of $F$ in which a pulse moves with a speed of $v$. Can someone show ...
pigsploof's user avatar
9 votes
1 answer
409 views

Motivating classical wave equation PDE

I'm teaching a geometry course covering spectral problems, using eigenvalues of the Laplace operator for shape analysis ("Can you hear the shape of a drum?"). I thought I'd cover where the wave ...
Justin Solomon's user avatar
0 votes
1 answer
148 views

Why does the wave equation need two ICs when the 'factored' wave equation needs only one?

The wave equation $$u_{xx}(x,t)=\frac {1}{c^2}u_{tt}(x,t) $$ requires two initial conditions because the equation is second order: IC1: $$u(x,0)= f(x)$$ IC2: $$u_{t}(x,0)= g(x)$$ But when it is ...
user45664's user avatar
  • 3,086
0 votes
1 answer
155 views

Wave equation as a consequence of Newton's second law

How the linear wave equation is a direct consequence of Newton's second law applied to any element of a string carrying a travelling wave?
GouravM's user avatar
1 vote
0 answers
117 views

Justification for using wave equation for describing a phenomena

I have recently started learning about waves. We didn't really formally describe what a wave is, but instead started by looking at a concrete example namely harmonic sinusoidal waves in 1d. We then ...
J.G95's user avatar
  • 11