# Traveling Wave Model: transverse wave on a string

## Homework Statement

A transverse wave on a string is described by the wave function: y=(0.120m)sin($$\frac{\Pi}{8}$$x+4$$\Pi$$t) 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

vy= -$$\omega$$Acos(kx-$$\omega$$t)
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
Mentor
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?

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
Mentor
What wavelength did you get?

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

Doc Al
Mentor
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.

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

Doc Al
Mentor
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.)

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