Is Total Energy Different from Energy Density for a 1D Standing Wave?

[cosine]

Here is a detail that makes me doubt:

Homework Statement

I am given the equation for a standing wave with a dependence in 't' and 'z' only... I am told that the wave is propagating in a confined space (2*2*2) m
Q1. Calculate the energy density for n=1,2,3. I didn't have any pb with this.
Q2. Calculate the total energy for n=1,2,3. (!)

Homework Equations

The Attempt at a Solution

Ok, I can't find anything in my lecture notes about total energy for waves. So I went back to the definition of energy density (h) which the amount of energy per unit of volume.
Therefore if I multiply the volume by h I should get the energy (right?)
The volume here is 8 m^3 BUT since the wave in question is only in 1 direction (z) do I still have to multiply by V or only by L=2m instead (for this particular case)

Thanks for your answer(s)

 

[dextercioby]

Well, since the integrated function has no "x" and "y" dependence, then the integration wrt them should be trivial, right ?

 

[cosine]

Well, since the integrated function has no "x" and "y" dependence, then the integration wrt them should be trivial, right ?

trivial... maybe not or perhaps I would not be posting...

The wave equation has no dependence in 'x' and 'y' indeed,however I am not integrated that function to get the total energy.
I got the energy density (Question 1) which is h = rho * (A*Omega/2)^2
A being the amplitude of the wave. The formula is correct according to my book (which does not mention total energy of sound waves btw)

If I check the units of 'h' I get J/m^3 therefore I should multiply by a volume to get the total energy (in J) trivial right? I guess that why I posted, I was surprised to get an energy density in J/m^3 calculated from a wave that's propagating in 1 direction only...