Power Supplied to a vibrating string

[Willjeezy]

Homework Statement

I keep getting the wrong answer for this question:

A taut spring for which μ = 0.05 kg/m is under tension of 80.0N. How much power must be supplied to the string to generate sinusoidal waves at a frequency of 60Hz and an amplitude of 6cm?

Homework Equations

ω = 2∏f
v = √(T/μ)
P = (1/2)μω²A²v

The Attempt at a Solution

Convert cm to m --> 6cm = 0.06m

Find ω
ω = 2∏(60)
= 376.99

Find v
v = √(80/.05)
=0.4m/s²

Find P
P = (1/2)(0.05)(376.99)²(0.06)²(0.4)
=5.12

however, the book tells me the answer is 512W. Did I convert something wrong?

Watts is J/s, and joules is in (Kg * m²)/s, so it only makes sense that I would have to convert the cm to m.

By dimensional analysis my answer has the units of :
(kg * rad² * m²) / s³

 

[TSny]

Find v
v = √(80/.05)
=0.4m/s²

Check this part of your calculation.

 

[Willjeezy]

blah...thanks.