Finding the wavelength on a sinusoidal wave on a string

[Andrew Jacobson]

Homework Statement

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."

Homework Equations

$k=2\pi/\lambda$
$y(x,t)=Acos(kx+\omega t)$

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.

 

[lep11]

Homework Statement

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."

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

(a) from reading off the graph you can see at the amplitude is 4mm or 0.004m

Correct

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

Correct

 

[Andrew Jacobson]

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

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.

 

[lep11]

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.

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