Analyzing a Traveling Wave: Frequency, Wavelength, and Direction

[hobmarcus]

Homework Statement

Two points on a string are observed as a traveling wave passes. The points are at x1 = 0 and x2 = 1 m. The two points are known to be less than one wavelength apart. The transverse motions of the two points are observed to be y₁=0.2 sin 3πt

y₂=0.2 sin (3πt+π/8)
(a) What is the frequency of this wave in hertz?(b) What is the wavelength?(c) What is the wave speed?(d) Can you tell if this wave is moving to the right or to the left? If so, which way is it moving?

The attempt at a solution

For part (a), I simply found the frequency by knowing that ω=3π and ω =2πf.
However, for part (b), I could not find the text's book answer by just using k=2π/λ
the answer's from textbook for b is

.

Any good explanations or hints for me? I have been reading the textbook again and again, but still can't find why.
(textbook = AP FENCH, vibrations and wave)

 

[vela]

How exactly did you use $k = \frac{2\pi}\lambda$?

 

[hobmarcus]

I assumed that π/8 = k and just find λ with k=2π/λ?

 

[vela]

Remember sin is periodic, so that's not the only possible solution.

 

[hobmarcus]

So.. what you mean is , I should assume that k=π/8 +2nπ ?

Also, how about part D? is there anyway to tell where is the wave going?