What is the relationship between wavelength and phase for mechanical waves?

[kpx001]

Homework Statement

The figure shows a snapshot of three waves traveling along a string, where x,t are in SI units. The phases for the waves are given by... the picture and problem is in this link
http://img339.imageshack.us/img339/2407/phys1prob.th.png

Homework Equations

(kx-wt)
lambda=2pi/k

The Attempt at a Solution

Basiclly I think I can solve the rest if i understand this problem. The wavelength= 2pi ?
but when i solve for k... k=2pi/lambda, k is one. the answer should give me that k is 2, and the only way i can get that is if the wavelength is pi. Can anyone please help me to understand this?

 

[kuruman]

If k = 2π / λ then the wave with the smallest k corresponds to the longest wavelength.

So ...

 

[kpx001]

I now understand the relationship, but I want to know how to do it the mathematical way.

 

[kuruman]

How do you mean "mathematical way"? The information that you are given is in a picture that you have to interpret.

 

[kpx001]

oh so it would be k=2n/lambda ... the 2n = 2(2pi) and the lambda = 2pi?

 

[kuruman]

... the 2n = 2(2pi) and the lambda = 2pi?

I don't know what you mean by this. The wavelength is inversely proportional to k. Therefore long wavelength means small k. Look at the picture. Which of the three waves has the longest wavelength? Then look at the phases. Which one has the smallest k, (a), (b) or (c)? Match the two. Continue with the other two waves.