Power of a wave at a specific point

[lizzyb]

Q: A wave pulse traveling along a string of linear mass density 0.0026 kg/m is described by the relationship $$y = A_0 e^{-bx}\sin(kx - \omega t)$$ where $$A_0 = 0.0097 m, b = 0.9 m^{-1}, k = .88 m^{-1} and \oemga = 56 s^{-1}$$. What is the power carried by this wave at the point $$x = 2.6 m$$?

Comments:
My book has: $$\wp = \frac{1}{2} \mu \omega^2 A^2 v$$ which is the "power associated with the wave" but yet we're to show "the power carried by this wave at the point x = 2.6 m". Plus the equation given isn't a normal wave function - I guess - since it has the coefficient $$e^{-bx}$$.

The book also has $$\wp = \frac{E_\lambda}{\Delta t}$$ so if I had a $$\Delta x$$ I could so something similar as before, that is $$\wp_{\Delta x} = \frac{E_{\Delta x}}{\Delta t}$$ but this isn't the same thing?

How should I proceed? thanks.

Edit:
I guess I could take as A the whole $$A_0 e^{-bx}$$ and plug it into the equation (using the given values)?

 

[OlderDan]

Edit:
I guess I could take as A the whole $$A_0 e^{-bx}$$ and plug it into the equation (using the given values)?

That should do it. A is a time-decaying amplitude in this case.

 

[lizzyb]

fantastic! thanks! :-)