PLEASE HELP! with Questions about a Traveling Wave?

Question

The wave function for a traveling wave on a taut copper wire of diameter 2 mm is y = y(x,t) = (0.15 m) sin (8π x - 120π t + π/4), where x is in meters and t is in seconds.

a) Find the wavelength, frequency, and speed of the wave.

b) Find the tension in the wire if the density of copper is 8.92

g/cm^(3),

c) Find the transverse velocity of a point on the wire at x=0

and t=0.

d) At what rate is the energy transmitted (the power) by this

wave along the wire?

The reason why I'm asking all this is because I have no idea how to work with this sine equation to find all the things that are asked. We always worked with cosine equations that describe the displacement of the string at different times. The given equation even has 3 terms inside the parentheses. I would really appreciate if you can please explain me a simple method on how to work with it.

Answer 1

If you know how to work with cosine equations, then transform this one with the identity:

sin u = cos (u - Pi/2)

Thereby changing your equation to

y(x,t) = (0.15 m) cos (8 Pi x - 120 Pi t - Pi/4)

Then work your magic, though it looks like you already know the answers. The only difference between a cos wave and a sin wave is a phase shift of 90 degrees which doesn't change any of your answers.