How Do You Calculate the Power Supplied to a Vibrating String?

[industry86]

--It is found that a 6.00m segment of a long string contains four complete waves and has a mass of 180g. The string is vibrating sinusoidally with a frequency of 50.0hz and a peak-to-valley distance of 15.0cm. (a) Write the function that describes this wave traveling in the positive x direction. (b) Determine the power being supplied to the string.--

Ok, I determined that w=2*pi*50hz=314 rad/s. k= (2*pi)/wave length=4.19rad/m (assuming that the 6m long segment with 4 equal length waves would give me a 1.5m wave length)

so i can answer (a), although having the A=6.00m is starting to bug me since the string is actually a lot longer that the segment experiencing the waves.

(b), is killin me though. I figure all i have to use is the P=1/2*u*w^2*A^2*v bit, but i can't seem to figure out v.
v=wave length*freq.
v=w/k
v=sqrt(period/u)

but if I use what I have determined previously, the first two equations come up with teh same answer, but the third one doesn't. the first 2 are 75m/s, the third is something like .81m/s. This makes me think that either my period, which I determined is .02s, is wrong, or something else is fundamentally wrong. And am I even using the right equation for the power?

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Um, since I don't know how to delete this post, I'll just correct myself here.

v=wavelength*freq
v=w/k
v=sqrt(TENSION!...not period/u)

please ignore this now

 

[bloopbloop]

*I'm just posting this despite the 6 year lapse for anyone else who will use this as future reference*

from part A, we know that
v = L/t
t = 1/f -> four complete waves -> 4/f
so v = (L * f)/4

however, for part B, in order to find the power throughout the string, we have to take the velocity from A and divide it by 4. so,
v = (L * f)/16

and yes, that was the right power equation.