Traveling Wave Model: transverse wave on a string

[mickellowery]

Homework Statement

A transverse wave on a string is described by the wave function: y=(0.120m)sin(\frac{\Pi}{8}x+4\Pit) Determine the transverse speed and acceleration of the string at t=0.200s for the point on the string located at x=1.60m. What are the wavelength, period, and speed of propagation of this wave?

Homework Equations

v_y= -\omegaAcos(kx-\omegat)
Since f=\frac{1}{T} and \omega is 4\Pi does that mean T=0.500?

The Attempt at a Solution

I was able to come up with -1.51 for the transverse speed, and I am pretty sure I understand why the acceleration is 0. I am having problems coming up with the wavelength and the proagation speed.

 

[Doc Al]

Since f=\frac{1}{T} and \omega is 4\Pi does that mean T=0.500?

Yes.

I am having problems coming up with the wavelength and the proagation speed.

Hint: How does k relate to the wavelength?

 

[mickellowery]

Hi Doc,

I had tried \lambda= \frac{k}{2\Pi} with k=frac{\Pi}{8} and it didn't work out to the right answer.

 

[Doc Al]

What wavelength did you get?

 

[mickellowery]

I got .0625m and the book says it should be 16m

 

[Doc Al]

Hi Doc,

I had tried \lambda= \frac{k}{2\Pi} with k=frac{\Pi}{8} and it didn't work out to the right answer.

That should be k ≡ 2π/λ.

 

[mickellowery]

So how does that change the relationship between k and \lambda? I couldn't write it as \lambda= \frac{k}{2\Pi}?

 

[Doc Al]

So how does that change the relationship between k and \lambda? I couldn't write it as \lambda= \frac{k}{2\Pi}?

No. If k = 2\pi / \lambda, then \lambda = 2\pi / k. (Just algebraic manipulation--but make sure you understand it.)

 

[mickellowery]

Oh alright I've got it now. It's those silly little math mistakes that get me every time. Thanks much Doc.