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Spherical waves

  1. Oct 27, 2007 #1
    what do we mean when we sy the speed of spherical waves is [tex]v[/tex]
     
  2. jcsd
  3. Oct 27, 2007 #2

    OOO

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    There are several definitions. Phase velocity, group velocity, front velocity. If there is no dispersion and no loss, all these give the same.
     
  4. Oct 27, 2007 #3
    when we write the equation of sphericcal wavefunctions [tex]\psi(r,t)=\frac{f(r-vt)}{r}[/tex] what does [tex]v[/tex] here mean
     
  5. Oct 27, 2007 #4

    OOO

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    As I said, if its a non-dispersive medium phase=group=front velocity. From your definition, f(x) represents a kind of wave group and so v is the group velocity. But on the other hand the term group velocity doesn't refer to spherical symmetry, but rather to pure translation. So maybe there is no established term for this.
     
  6. Oct 27, 2007 #5

    jtbell

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    Staff: Mentor

    It means the same thing as with a plane wave. If you "stand" at a fixed location anywhere and watch the wavefronts (surfaces of constant phase) go past you, they are moving at speed [itex]v[/itex].

    (By the way, equations embedded into text line up better with the text if you use "itex" instead of "tex" in the tags.)
     
  7. Oct 27, 2007 #6
    thanks
     
  8. Oct 27, 2007 #7

    rbj

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    not necessarily if you're viewing with Firefox on linux or Mac.
     
  9. Oct 27, 2007 #8

    jtbell

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    Staff: Mentor

    I'm using Firefox (2.0.0.1) on a Mac (OS 10.4.10) right now. I haven't noticed any problems with the last few versions (at least) of either of these.
     
  10. Oct 27, 2007 #9

    rbj

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    testing [itex]1, 2, 3[/itex] ...

    hmmm, looks like you're right. i'm using my daughters' iMac.

    but i'm pretty certain, using Firefox under Fedora linux, (which is what i have at work), that even with itex, the expressions get elevated a little from the baseline of the text.
     
    Last edited: Oct 27, 2007
  11. Oct 27, 2007 #10
    @jtbell
    well one doubt more
    then can we define wavefunctions as functions which satisfy
    [tex]\Nabla^{2}=\frac{\delta^{2} \psi}{v^{2}\delta t^{2}}[/tex] for some constant [itex]v[/itex] whixh sometimes turns out to be the phase velocity or for that matter group or front velocity
     
  12. Oct 29, 2007 #11

    rbj

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    jt, i just happened to check, and it's:

    the itex baseline is elevated about 1/2 line above the regular text baseline. dunno why that is, but i've been less impressed with linux than the hacker community.
     
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