- #1
Andy365
- 2
- 0
Hello,
consider a 1D elastic wave which have the amplitude:
[tex]A=cos(x)[/tex]
What is the energy density: [tex]\frac{dE}{dx}[/tex] of this wave?
I seem to recall that the energy of a wave is proportional to the square of the amplitude:
[tex]E \propto A^2[/tex]
That seem to mean that [tex]\frac{dE}{dx} \propto cos(x)^2[/tex]
However the energy density should be constant for all x in this case, since there is no loss!?
If I instead define [tex]A=e^{ix}[/tex], and use that [tex]E \propto |A|^2[/tex]
things work better since [tex]|A|^2 = 1[/tex], which is independent of x.
So what is happening here?
Thanks in advance for any answers!
consider a 1D elastic wave which have the amplitude:
[tex]A=cos(x)[/tex]
What is the energy density: [tex]\frac{dE}{dx}[/tex] of this wave?
I seem to recall that the energy of a wave is proportional to the square of the amplitude:
[tex]E \propto A^2[/tex]
That seem to mean that [tex]\frac{dE}{dx} \propto cos(x)^2[/tex]
However the energy density should be constant for all x in this case, since there is no loss!?
If I instead define [tex]A=e^{ix}[/tex], and use that [tex]E \propto |A|^2[/tex]
things work better since [tex]|A|^2 = 1[/tex], which is independent of x.
So what is happening here?
Thanks in advance for any answers!