# Recent content by Nick Jackson

1. ### Are waves always the sum of sine waves?

I saw that somewhere and it is supposed to be something Fourier came up with but I can't find somewhere why... Please explain (with mathematical description if possible)
2. ### Deriving the formula for sine waves

Chestermiller, if you're reffering to the d'Alembertian, I've already mentioned that the equation is correct for these result that are a function of x+vt and x-vt. However, my point is that to know if a sine wave is such we have to either observe it from experiments or to predict it...
3. ### Deriving the formula for sine waves

Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...
4. ### Integration of factorials

Sorry I meant to put r in the variable not k. However I see your point about the continuity... I started with having sums in the lhs and the rhs. What do I do now?
5. ### Integration of factorials

Hello, well here's my problem: I got this integral and I don't know how to calculate it (I am trying to find if there exists a k that satisfies this relation) : \int_0^k \frac{1}{ ( 4k-4r-2 ) ! ( 4r+1 ) ! }\, \left ( \frac{y}{x} \right )^{4r} dk = \int_0^k \frac{1}{ ( 4k-4r ) ! ( 4r+3 ) ! }\...
6. ### Confusion with integration of sums

Oh i get it! Thanks a lot!
7. ### Confusion with integration of sums

Hello guys, since I am new at sums and multivariable calculus I faced a problem when I stumbled upon this: \sum_{r=0}^{k} \binom{n}{4r+1} x^{n-4r-1} y^{4r+1} = \sum_{r=0}^{b} \binom{n}{4r+3} x^{n-4r-3} y^{4r+3} Well, the problem is that I don't know if it's possible to put a limit in every...
8. ### Proof of Fermat's principle of least time?

I've been looking for this proof for months but I wasn't able to find something...
9. ### Change of spin during dipolar bond

OK so we have a dipolar bond between two elements. This bond makes the other electrons redistribute in order to rest in peace. Everything's OK up until now. What happens, however, when two of these other electrons have the same spin an yet they end up together because of this redistribution? I...
10. ### Why is spin number half integer, especially +1/2,-1/2 for electrons?

Ok guys, I know this must be pretty basic for but I am new to this section of physics. Anyway, my question is a two-part one, I guess: 1) Why does the spin number get only half integer values in fermions and integer values in bosons, mesons, etc.? 2) How do we conclude that the spin number is...
11. ### Proof of Fermat and Huygens–Fresnel principle

Hey guys, I don't know if here is the right section for this question but anyway. So I was looking for the proof or derivation of the Fermat's principle and all I got was the Huygens–Fresnel principle. However, neither could I understand how the Huygens–Fresnel principle derives the Fermat's...
12. ### Bohr's atomic model and Bohr and Rydberg equations

Thank you very much for your answer, it has been very helpful and the expansion of the Bohr's model answers many of my questions in general. Unfortunately, even with the resource you provided me with, I can't conclude why the mathematical statement stays intact... Thanks very much anyway!! :)
13. ### Bohr's atomic model and Bohr and Rydberg equations

Hello, well, I am totally new to this section of physics so my question may sound ridiculous, but here it is: When I was reading about the Bohr's atomic model, I learned about the Bohr and Rydberg equations (E=-2,18*10^18*Z^2/n^2 J and 1/λ=RZ^2(1/n1^2-1/n2^2) as well as their proofs. Then I...