Think about the sound waves like longitudinal waves, with different concentrated points a certain distance from each other. The distance between these waves is what determines the pitch, closer = higher and farther = lower. Now if these waves are moving toward a person who's moving away from...
Wonderful! :D
Also, if I messed up somewhere it would've been with the \int_0^R e^{-r/a} r^2 dr, and that just becomes the 2a^3 - e^{-R/a}(a R^2 + 2 a^2 R + 2 a^3) after an s=-r substitution, and then integrating by parts twice to get e^{s/a} alone in an integral, correct? ^-^
By the...
Lol, I've only done Calc I. :X But wow! I had no idea you could do that with the integrals, that makes it MUCH more understandable. :D That was my main problem for sure, though after working through it that \int_0^R e^{-r/a} r^2 dr was a little tricky, but I think I got it figured. ^-^...
Sorry, I just wasn't grasping it (still not sure if I am). I'm not familiar on how to integrate variables in terms of other variables (i.e integrating \phi in terms of r and vice versa), it's just something that wasn't possible in calc I. If it was deriving, you'd simply make it a derivative...
Alright, still all sounds fairly confusing, but I'm going to try to work through it on paper, and I'll post what I get. (still all seems a bit tough for calculus based physics 1 :( )
Feel free to post any other suggestions or comments if anyone has one, they all help!
<3's
Pretty much worked out, but stuck! Gauss' Law problem
Homework Statement
"Consider a charge density distribution in space given by \rho = \rho_0 e^{-r/a}, where \rho_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r...
Lol, well like I said, I haven't quite grasped integrating in physics. Math is easy since variables there don't usually actually stand for anything. I have made some mistakes in the past in this area, and usually learn from them best by seeing the correct answer and being able to compare mine to...
Ahh, alright, I'll try that! Thanks.
Though this is my worst subject in physics (though you can probably tell? :( ) and I'm REALLY bad at integrating in physics, great at it in math, but have trouble grasping it in physics for some reason. I also have to leave for a couple hours, so (if you...
Thank you! :D That's a much more understandable way to show it for me (math major).
I was looking over what you just explained and looking back at what I did the post beforehand and I think that's actually what I attempted to do, but I'm not 100% sure I did it all right, and is it okay to...
I played around with it algebraically and brought in Coulomb's Law, E = 1/(4*[pi]*[epsilon]_0)*q/r^2, and [rho] = q/V, and got [rho] = (E*4*[pi]*[epsilon]_0*r^2)/V, and using volume of a circle = 4/3[pi]r^3, I was able to eliminate a lot, ending up with [rho] = (3*E*[epsilon]_0)/r.
And bringing...
Sorry about the delay, was having some connection issues. :X
And that all does sound very familiar, not sure I completely grasped it all though, if someone doesn't mind going through it or doing a step or two in the right direction (I learn best through example) that might be a bigger help...
Homework Statement
"Consider a charge density distribution in space given by [rho] = [rho]_0 * e^(-r/a), where [rho]_0 and a are constants. Using Gauss' Law, derive an expression for the electric field as a function of radial distance, r. Sketch the E vs. r graph.
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