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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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