Power Supplied to a vibrating string

AI Thread Summary
The discussion revolves around calculating the power required to generate sinusoidal waves on a taut spring with specific parameters. The user correctly identifies the equations needed, including the angular frequency (ω), wave speed (v), and power (P). However, the user arrives at a power value of 5.12W, while the textbook states the answer should be 512W. The discrepancy suggests a potential error in the calculations, particularly in determining the wave speed or power formula application. The conversation emphasizes the importance of unit conversion and accuracy in calculations for physics problems.
Willjeezy
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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
 
Last edited:
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Willjeezy said:
Find v
v = √(80/.05)
=0.4m/s2
Check this part of your calculation.
 
blah...thanks.
 

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