Power carried by a damped wave pulse on a string

[MissPenguins]

Homework Statement

A wave pulse traveling along a string of linear mass density 0.0043 kg/m is described by the relationship
y = A₀ e ^{−b x} sin(k x − ω t) ,
where A₀ = 0.0032 m, b = 0.68 m ⁻¹ , k = 0.57 m ⁻¹ and ω = 44 s ⁻¹ .
What is the power carried by this wave at
the point x = 2.2 m?
Answer in units of W.

Part b
What is the power carried by this wave at the origin?
Answer in units of W.

Part c
Compute the ratio P/P₀ .

Homework Equations

v = w/k
P=1/2 $$\mu$$w²A²v

The Attempt at a Solution

v=w/k => 44s^-1/0.57m^-1=77.19 m/s

Plug it in the Power equation
P=1/2 (0.0043kg/m)(44s^-1)²(0.0032 m)²(77.19 m/s) = 0.00329 W

Can someone please let me know if I am on the right track? I feel like it's wrong since e is added this time. I feel like I have to do some derivative. Thank you!

 

[vela]

The Attempt at a Solution

v=w/k => 44s^-1/0.57m^-1=77.19 m/s

Plug it in the Power equation
P=1/2 (0.0043kg/m)(44s^-1)²(0.0032 m)²(77.19 m/s) = 0.00329 W

Can someone please let me know if I am on the right track? I feel like it's wrong since e is added this time. I feel like I have to do some derivative. Thank you!

Your calculation looks fine to me. What do you mean by "e is added this time"?

If you want to use TeX to write symbols, you should use it for the entire expression instead of just for individual symbols. It's easier for you and it'll look nicer.

 

[MissPenguins]

Your calculation looks fine to me. What do you mean by "e is added this time"?

If you want to use TeX to write symbols, you should use it for the entire expression instead of just for individual symbols. It's easier for you and it'll look nicer.

So is my approach correct?

 

[vela]

Yup, looks good to me.

 

[MissPenguins]

I submitted the answer, and it's wrong! :(

 

[vela]

Oh, I'm sorry. I totally overlooked the decaying exponential. I take it that's what you meant by "e is added this time."

The formula for the power you used is for the average power of a regular sinusoidal wave traveling on the string. You don't have that here, so it's not applicable.

 

[vela]

So presumably you've seen the derivation of the power formula. What you need to do is use those same concepts to figure out the power in this problem.

You might also find this web page helpful:

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/powstr.html#c2