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! :-)