# Homework Help: Finding the wavelength on a sinusoidal wave on a string

1. Mar 31, 2015

### Andrew Jacobson

1. The problem statement, all variables and given/known data
Hi, this is a problem regarding mathematical descriptions of waves. I've attached an imagine of the picture but I'll also type out the problem for clarity.
"A sinusoidal wave is propagating along a stretched string that lies on the x-axis. The distplacement of the string as a function of time is graphed in Fig.E11 for particles x=0m and at x=0.09m. (a) What is the amplitude of the wave? (b) What is the period of the wave? (c) You are told that the two points x=0 and x=0.09 are within one wavelength of each other. If the wave is moving in the +x-direction, determine the wavelength and wave speed."
2. Relevant equations
$k=2\pi/\lambda$
$y(x,t)=Acos(kx+\omega t)$

3. The attempt at a solution
(a) from reading off the graph you can see at the amplitude is 4mm or 0.004m

(b) from reading off the graph you can see that the period = 0.04s

(c) this is where I got confused. I thought about making simultaneous equations using x=0 and x=0.09. I figure that the answer involves using the fact that $k=2\pi/\lambda$ but I'm a little unsure.
I started playing with the idea that when y=0 and t=0 $0.004cos(kx)=0$ and therefore $cos(kx)=0$ and $kx=n\pi/2$ however that's not particularly helpful since I don't know the value of x. If anyone could give me a hint or put me on the right track it'd be much appreciated.

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• ###### 20150331_130354[1].jpg
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2. Mar 31, 2015

### lep11

Wouldn't this mean the wavelength is 0.09m?
How are frequency, wavelength and speed related?

Correct
Correct

3. Mar 31, 2015

### Andrew Jacobson

Well it just says that they're within one wavelength, so the wavelength could be bigger than 0.09m? I know that $v=\lambda f$ but this doesn't help since I only know the frequency.

4. Mar 31, 2015

### lep11

Oh, my bad, I thought the points are one wavelength away from each other. Anyway, v=λf=λ/T still holds.

Last edited: Mar 31, 2015