Find factor of the power increase?

[blackbyron]

Homework Statement

A periodic wave on a string has a frequency 178Hz and an amplitude 7.9cm. The wave speed in the string is 8.8m/s and the linear mass density is 0.0008kg/m. Power in a wave is proportional to the square of the amplitude and the square of the frequency. If the frequency increases by 177%. By what factor will the power increase?

Homework Equations

So P is proportional to the square of the amplitude and the square of the frequency.
which is P = A^2 * f^2, right?

frequency = 178Hz
177% increase of frequency = 493.06Hz

y'(t) = Aw(sin(kx-wt))

The Attempt at a Solution

Do I use P = A^2 *f^2 to find the factor, if so, then I how am I going to solve for A2 for 1.77 increase?

My physics teacher, didn't make the notes clear, so I tried to keep googling on the problem relate to this, but I couldn't

Any help would be appreicated

 

[anathema]

Thank you for your question. You are correct in your equation for power, P = A^2*f^2. To find the factor by which the power will increase, we can set up a ratio between the new power and the original power:

(P2/P1) = (A2^2*f2^2)/(A1^2*f1^2)

Since we are given that the frequency increases by 177%, f2 = 1.77*f1. We also know that the amplitude remains constant, so A2 = A1. Substituting these values into the equation, we get:

(P2/P1) = (A1^2*f1^2)/(A1^2*(1.77*f1)^2) = 1/(1.77)^2 = 0.318

Therefore, the power will increase by a factor of 0.318 or approximately 32%.

I hope this helps clarify the problem for you. If you have any further questions, please don't hesitate to ask.