wave equation

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January 26th 2009, 06:10 AM
James0502

wave equation

Let
E
:=1/2(Tyxx+ ½ytt ) and P := Tyxyt.

Show that
Et = Px and TEx = ½Pt

and deduce that
E and P are also solutions of the wave equation, i.e.

TE
xx = ½Ett and TPxx = ½Ptt.

What are the physical interpretations of
E and P?

I am unsure of this, the physical interpretation of E and P.. are they the nodes?

many thanks
January 28th 2009, 12:54 AM
InvisibleMan

Well my guess is that E is the total energy and P total momentum of the wave, you can check for units if they are the same ones as they should be, anyway that's my guess.
January 31st 2009, 06:31 AM
Danny

Quote:

Originally Posted by James0502

Let

E

:=1/2(Tyxx+ ½ytt ) and P := Tyxyt.

Show that

Et = Px and TEx = ½Pt

and deduce that

E and P are also solutions of the wave equation, i.e.

TE

xx = ½Ett and TPxx = ½Ptt.

What are the physical interpretations of

E and P?

I am unsure of this, the physical interpretation of E and P.. are they the nodes?

many thanks

Are you sure on
$<br /> E= \frac{1}{2} \left(Ty_{xx}+\frac{1}{2}y_{tt} \right)$ ?

I mean the second order derivatives.