# Traveling Wave Model: transverse wave on a string

1. Jun 24, 2010

### mickellowery

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
vy= -$$\omega$$Acos(kx-$$\omega$$t)
Since f=$$\frac{1}{T}$$ and $$\omega$$ is 4$$\Pi$$ does that mean T=0.500?

3. 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.

2. Jun 24, 2010

### Staff: Mentor

Yes.

Hint: How does k relate to the wavelength?

3. Jun 24, 2010

### 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.

4. Jun 24, 2010

### Staff: Mentor

What wavelength did you get?

5. Jun 24, 2010

### mickellowery

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

6. Jun 24, 2010

### Staff: Mentor

That should be k ≡ 2π/λ.

7. Jun 24, 2010

### mickellowery

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

8. Jun 24, 2010

### Staff: Mentor

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

9. Jun 24, 2010

### mickellowery

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