Search results

  1. F

    Calculate flux from a radiating disk

    Actually, something that doesn't make sense to me...why is it that my first attempt at the problem (see original post) gives you the same answer even though we're treating the flux as though it were crossing some spherical region and not a plane?
  2. F

    Calculate flux from a radiating disk

    Well thank you so much for the help!
  3. F

    Calculate flux from a radiating disk

    My latest thoughts: F = \int{I cos^2\theta dA/\rho^2} dA = 2\pi \rho d\rho F = 2\pi I \int{cos^2\theta d\rho /\rho} = 2\pi I \int{cos^3\theta d\rho /z} = 2\pi I \int{cos\theta sin\theta d\theta} = -I\pi cos^2\theta Or, when evaluated from 0 to pi/2: F = I\pi And I think this is where you...
  4. F

    Calculate flux from a radiating disk

    Ok, great. So then I think up to here I'm good: F = \int{I cos^{2}\theta dA / \rho^2} One thing that just occurred to me from my last post is that dA is the infinitesimal area through which the flux is being calculated, in our case, the plane at z=Z. I was treating it as an infinitesimal area...
  5. F

    Calculate flux from a radiating disk

    It seems like we disagree right off the bat with the equation for flux? Isn't this how it's defined in radiative processes? Where d\Omega = dA/r^2. dA is an "infinitesimal amount of surface area that is located a distance r from the source and oriented perpendicular to the position vector r."...
  6. F

    Calculate flux from a radiating disk

    \rho^2 = r^2 + z^2 2\rho d\rho = 2rdr since z is constant. I think I understand most of your reasoning, but I'm still not sure how to go about the problem. A disk as viewed from some point P that is off axis will appear as an ellipse -- ok, that much makes sense. So that means the projected...
  7. F

    Calculate flux from a radiating disk

    Hm, ok. Let's see... F = \int{I \cos{\theta} d\Omega} d\Omega = dAcos{\theta}/\rho^2 F = I \int{cos{\theta} dA cos{\theta}/\rho^2} cos{\theta} = z/\rho F = I \int{(z/\rho)^2 dA/\rho^2} = I \int{(z/\rho)^2 2\pi r dr/\rho^2} = 2\pi I z^2 \int{\rho d\rho / \rho^4} = -\pi I z^2/\rho^2 Not sure...
  8. F

    Calculate flux from a radiating disk

    Ok...so is what I did above in calculating the flux not the same? The cos term arrises from the projection into the line of sight direction. I am incredibly confused.
  9. F

    Calculate flux from a radiating disk

    Ah, should just be the projected area, right? A*cos(theta)?
  10. F

    Calculate flux from a radiating disk

    Ok, fair enough. That being said, I don't think I understand the drawing. I'm not sure what that length (perpendicular from X1 to QX2 is? Thanks for the help by the way!
  11. F

    Calculate flux from a radiating disk

    Ok, I think you're essentially asking me to do this (page 32), right? I don't think I fully grasped the concept of solid angle. It's the differential of the projected area (projected onto the direction of the observer) divided by the radius of a sphere squared. So, above, I was regurgitating the...
  12. F

    Calculate flux from a radiating disk

    In general, it would be A/t^2, right?
  13. F

    Calculate flux from a radiating disk

    Added some work to my last post. Bumping this in case anyone is able to help further. Thanks!
  14. F

    Calculate flux from a radiating disk

    Ah, you mean expressing the solid angle in cylindrical coordinates and in turn the flux? So d\Omega ={z d\phi d\rho}/\rho^{2}? The problem also says that by assuming Z>>r, you can use the small angle approximation, so in the expression for flux can I let cos\theta = 1, and then F is entirely in...
  15. F

    Calculate flux from a radiating disk

    Homework Statement Suppose you have a disk of radius r at x=y=z=0 with its normal pointing up along the z-axis. The disk radiates with specific intensity I(\theta) from its upper surface. Imagine the observer plane is at z=Z, where Z is much greater than r. Let I(\theta) = I = constant...
  16. F

    Determine the state of a particle

    I thought it was realated via: |+x> =1/\sqrt{2} (|+z> + 1/\sqrt{2} (|-z> but I'm not sure how this changes for |-x>.
  17. F

    Determine the state of a particle

    Thanks for the reply. You're right, I missed the square roots on z-basis expression. Thanks! I haven't checked whether \Psi is really the same. I know that the inner product of \Psi with itself should give me 1 (if indeed it's the same). But wouldn't I need to somehow go between x and z to do...
  18. F

    Determine the state of a particle

    Homework Statement It is known that there is a 36% probability of obtaining S_z = \hbar/2 and therefore a 64% chance of obtaining S_z = -\hbar/2 if a measurement of S_z is carried out on a spin 1/2 particle. In addition, it is known that the probability of finding the particle with S_x =...
  19. F

    Graduate Programs for Radio Astronomy

    Excellent, thanks!
  20. F

    Graduate Programs for Radio Astronomy

    Hello all, I'm trying to compile a list of schools (mainly in the US) that offer Ph.D. programs with research in radio astronomy. Here's what I've come up with so far: Caltech Cornell Harvard New Mexico Tech Ohio State University UC Berkley UC Los Angeles UC Santa Cruz University of Arizona...
  21. F

    Anyone applied for summer 2014 internships/fellowships yet?

    Thank you. You never know, though! Hang in there!
  22. F

    Anyone applied for summer 2014 internships/fellowships yet?

    They did wind up offering me a position.
  23. F

    Anyone applied for summer 2014 internships/fellowships yet?

    I've heard from ASTRON, Harvard, NRAO, but nothing else.
  24. F

    Wave Equation for a Vibrating String

    Hm, I was able to work through the problem, correcting for the period, and it looks like I'm now only off by a factor of 2. A friend of mine is also having the same problem. Not sure if we can chalk it up textbook error, or just something we're not seeing... Ah nevermind, feeling rather silly...
  25. F

    Wave Equation for a Vibrating String

    Hm, ok, fair enough. Thank you so much for all the help. I knew it was going to come down to something silly.
  26. F

    Wave Equation for a Vibrating String

    Yep, I just got that. Makes sense now. Thank you so much! Although, can I ask, how would one know (without knowing the answer) that the period is in fact 2l and not l, like I wrongly assumed it was, just from reading the problem/looking at the image. Ah man, feeling rather stupid.
  27. F

    Wave Equation for a Vibrating String

    http://en.wikipedia.org/wiki/Fourier_series Everything I've looked up suggests the 2 should be there. I'm also pretty sure I've been using the 2 in all my fourier coefficients calculations up until now. :( I thought the two arises from the fact that ω=2pi/T. I'm sorry. I guess I'll run...
  28. F

    Wave Equation for a Vibrating String

    I'm almost certain the 2pi factor belongs there. At least it certainly does in the equations for the coefficients of a fourier series, where the 2pi emerges from ω. Unless for some reason those equations are modified in this case? I know the book tends to leave off the 2pi, but that's when...
  29. F

    Wave Equation for a Vibrating String

    So actually, my An includes the prefactor of 2h/\pi^{2}. There's on the other hand, is independent of the constants out front. That's why I was thinking that maybe the two answers are equivalent, in that they factored those pre-factors out, but then the fact that our sin terms are different is...
Top