How to solve for power in a piano wire wave problem?

AI Thread Summary
To solve for the average power in a piano wire wave problem, the relevant equation is P = 0.5 * sqrt(μ * F) * (ω^2) * A^2. The mass of the wire must be converted to kilograms, and the length to meters to calculate the linear mass density (μ). The tension (F) is given in Newtons, while the amplitude (A) must be converted from millimeters to meters. After ensuring all units are correct, substituting these values into the equation should yield the correct answer, which is approximately 0.3 W. Proper unit conversion is crucial for solving this problem accurately.
DGalt
Messages
4
Reaction score
0

Homework Statement


A piano wire with mass 3.25 g and length 84.0 cm is stretched with a tension of 27.0 N. A wave with frequency 100 Hz and amplitude 1.30 mm travels along the wire.


Homework Equations


The only equation that I think applies to this one is P = .5*Sqrt(μ*F)*(omega^2)*A^2


The Attempt at a Solution


I've tried this freaking problem five times now, and I'm down to my last try on Mastering Physics (online homework program).
I thought this was a pretty straightforward problem. I started out solving for μ by basically converting the mass (3.25g) to kg and the length (84cm) to m and then dividing the mass by the length. I solved for omega with the equation omega = frequency * 2PI. F I'm assuming is the tension.

Then I thought it was simply a plug-in problem, but I can't seem to get it right. I had to do five different trials because at first I solved for μ wrong and then I wasn't sure what units the program wanted it in (just had Watts next to the solution, so I just assumed i needed to put everything into kg and m and all that stuff). But yea, I don't know what I'm doing wrong.

If anyone can help me out on this one I'd appreciate it, just can't seem to figure out what went wrong

thanks in advance
 
Physics news on Phys.org
What's the question?
 
woops...yea I'm an idiot
The question is:
Calculate the average power carried by the wave.
 
what answers have you tried
 
i have the exact same question on my Mastering Physics homework, and I just figured it out. You use that equation and just plug everything in, but the units must be converted for almost everything. So the mass must be in kg, length must be in meters, tension is in N already, frequency is in Hz already, but amplitude must be in meters (not mm). Once you convert everything and plug it into the equation, you get the right answer (mine was about 0.3 W, my numbers may be different than yours though!) For the part B, you just do (1/2) of the amplitude when plugging it in!

Good luck!
 
Clarification? what did you change the formula into?
 
I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
Thread 'A cylinder connected to a hanging mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top