Speed of Spherical Waves: How Fast is v?

[pardesi]

what do we mean when we sy the speed of spherical waves is $$v$$

 

[OOO]

what do we mean when we sy the speed of spherical waves is $$v$$

There are several definitions. Phase velocity, group velocity, front velocity. If there is no dispersion and no loss, all these give the same.

 

[pardesi]

when we write the equation of sphericcal wavefunctions $$\psi(r,t)=\frac{f(r-vt)}{r}$$ what does $$v$$ here mean

 

[OOO]

when we write the equation of sphericcal wavefunctions $$\psi(r,t)=\frac{f(r-vt)}{r}$$ what does $$v$$ here mean

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.

 

[jtbell]

when we write the equation of sphericcal wavefunctions $$\psi(r,t)=\frac{f(r-vt)}{r}$$ what does $$v$$ here mean

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 $v$.

(By the way, equations embedded into text line up better with the text if you use "itex" instead of "tex" in the tags.)

 

[pardesi]

thanks

 

[rbj]

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 $v$.

(By the way, equations embedded into text line up better with the text if you use "itex" instead of "tex" in the tags.)

not necessarily if you're viewing with Firefox on linux or Mac.

 

[jtbell]

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.

 

[rbj]

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.

testing $1, 2, 3$ ...

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.

 

[pardesi]

@jtbell
well one doubt more
then can we define wavefunctions as functions which satisfy
$$\Nabla^{2}=\frac{\delta^{2} \psi}{v^{2}\delta t^{2}}$$ for some constant $v$ whixh sometimes turns out to be the phase velocity or for that matter group or front velocity

 

[rbj]

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.

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

Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.8.0.7) Gecko/20060913 Fedora/1.5.0.7-1.fc5 Firefox/1.5.0.7 pango-text

the itex baseline is elevated about 1/2 line above the regular text baseline. don't know why that is, but I've been less impressed with linux than the hacker community.