Recent content by fuserofworlds

I did, but am still a little confused, though I think I am closer to understanding. If there were a system of two particles each with their own coordinates, and you wanted to compute ∂U/∂x, you would just do it with respect to a given origin, correct? What confuses me is that, if (as in the...

I realize I phrased that wrong. What I mean is, in general your function for the potential will be a function of ##\vec{r}## in general, or U(x,y,z). Mathematically, how does one then take ##(\partial U/\partial x_1, \partial U/\partial y_1, \partial U/\partial z_1)##, and how is that...

I understand that it refers to the coordinates of particle one, but I don't see why this is necessary. Isn't the derivative taken with respect to the axes? x, y, and z are variables and ##\vec{r}_1## is the position of particle one. If I take the derivative with respect to ##x_1##, aren't I...

I'm currently going over some mechanics notes and am confused about the following situation: In the book I'm looking at, it describes two particles absent of external forces, only exerting a force on each other. In deriving a potential energy equation for the two, it goes on to say that if the...

I just completed a brief introduction to branch points in complex analysis, and I find it difficult to imagine/come up with functions with nonzero branch points. My difficulty is this: for the point to be considered a branch point, f(r,θ) and f(r,θ+2π) must be different for ANY closed path...

Thank you, that makes sense!

I was reviewing the infinite square well, using D.J. Griffiths, and came across this small point of confusion. The time-independent solution is shown to be Asin(kx), where the constant A is determined by normalization. Then, in assembling the complete (time dependent) solution, he writes that...

vela and j824h, thank you, that makes sense!

This is the example in my book. I understand that we now know light has the same speed in any reference frame; but the book seems to imply that this is only because light does not travel through a medium. What am I getting from the book is that, for a wave traveling in a medium, if the source...

So, are you saying that in special relativity, the speed of sound (or of any wave) measured relative to the medium DOES depend on the speed of the source?

vela, sorry for the confusion. The book makes it clear that the waves must be measured relative to still air. To me, this implies to me that if the air (the medium) were moving, you would measure a different speed. Because inertial reference frames are identical, you would likewise measure a...

So, I am reading my Modern Physics textbook (Tipler & Llewellyn), in the chapter on relativity. In discussing the Michelson-Morley experiment, the book states, "The speed of the waves depends on the properties of the medium and is derived relative to the medium. For example, the speed of sound...