- #36
snoopies622
- 840
- 28
Well atyy, after having spent more time this weekend struggling with this puzzle than I care to admit, I now think you're right about the minus signs.
The energy of a wave should be
[tex]
E = \mid 2 \pi ^2 f T A^2 v^{-1} \mid
[/tex]
while its momentum is
[tex]
p = \frac { \mid 2 \pi ^2 f T A^2 v^ {-1} \mid } {v}
[/tex]
where [tex] v [/tex] is either positive or negative depending on the wave's direction. This seems to make everything work out.
Part of my confusion came from substituting terms back and forth between the wave-at-a-boundary equations (where 1/v can be either positive or negative) and the colliding ball equations (where mass is always positive). I'm still not clear about how far one can take that sort of thing, but for now I believe that there is something left there for me to discover and I find it very alluring.
Anyway, thanks for your help.
The energy of a wave should be
[tex]
E = \mid 2 \pi ^2 f T A^2 v^{-1} \mid
[/tex]
while its momentum is
[tex]
p = \frac { \mid 2 \pi ^2 f T A^2 v^ {-1} \mid } {v}
[/tex]
where [tex] v [/tex] is either positive or negative depending on the wave's direction. This seems to make everything work out.
Part of my confusion came from substituting terms back and forth between the wave-at-a-boundary equations (where 1/v can be either positive or negative) and the colliding ball equations (where mass is always positive). I'm still not clear about how far one can take that sort of thing, but for now I believe that there is something left there for me to discover and I find it very alluring.
Anyway, thanks for your help.