Equations · Physics
Wave equation
How a disturbance travels through a medium at speed c.
∂²u/∂t² = c² ∇²u
Aethel says
the second partial derivative of u with respect to t equals c squared times the Laplacian of u
What it says
The acceleration of the displacement u at each point is proportional to how curved the displacement is around it. The result is a wave moving at speed c without changing shape.
The same equation describes sound, vibrating strings and, in vacuum, light.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| u | u | the displacement at each point and time |
| ∂²u/∂t² | the second partial derivative of u with respect to t | the acceleration of the displacement |
| ∇² | the Laplacian of | the sum of second derivatives in every direction |
| c | c | the wave speed |
Where you meet it
Physics and engineering courses on waves and partial differential equations.
Questions
How do you say Wave equation out loud?
∂²u/∂t² = c² ∇²u is read: “the second partial derivative of u with respect to t equals c squared times the Laplacian of u.” That is exactly what Aethel says when it meets the formula in a book.
What does u mean in Wave equation?
u (said “u”) is the displacement at each point and time.
What does ∂²u/∂t² mean in Wave equation?
∂²u/∂t² (said “the second partial derivative of u with respect to t”) is the acceleration of the displacement.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.