- #1

JoeyBob

- 256

- 29

- Homework Statement
- y(x, t) = 0.2 sin(0.25x-12t). Find horizontal velocity as a function of time at x=4

- Relevant Equations
- none

This is more of a conceptual question. To find the horizontal velocity as a function of time for the above wave function, you take its partial t derivative and insert x=4. In other words the function would be -2.4sin(1-12t).

Im wondering why you take the partial t derivative and not to partial x derivative? I understand how partial derivatives work, but I still don't think I am entirely sure what they represent. Like, why can't you take the partial x derivative? Wouldnt the change in x be about velocity? What does a partial t derivative actually mean / represent in this context? Horizontal velocity, but why/how?

Im wondering why you take the partial t derivative and not to partial x derivative? I understand how partial derivatives work, but I still don't think I am entirely sure what they represent. Like, why can't you take the partial x derivative? Wouldnt the change in x be about velocity? What does a partial t derivative actually mean / represent in this context? Horizontal velocity, but why/how?