Solving 4-Vectors and Wave Amplitudes in Different Frames

[captainjack2000]

Homework Statement

I am aving a bit of trouble understanding how to show something is a 4 vector. For example K = (v/c, 1/lamdba, 0, 0 ) Show it is a 4-vector. I am not quite sure how to start this.
Similarly I have the amplitude of a wave in frame S described as A=cos[2PI(vt-x/lambda)] and need to show that the amplitude of te wave in S' can be written as cos[2PI(v't'-x'/lambda')

Homework Equations

The Attempt at a Solution

I am not sure how to do the first part

My attempt at the second part
vt-x/lambda
= vct/c - x/lambda
=v/c(gamma(ct'+beta x')) -1/lambda *gamma(x'+beta ct')
=ct' gamma(v/c-beta/lambda)-x'gamma (1/lambda-beta v/c)
using a similar question in my notes but I don't think this is right and I don't know how it helps?

 

[aurora14421]

I think we do this question by showing that K transforms by a Lorentz transformation (since the definition of a 4 vector is a 4 component vector that transforms under Lorentz transformations).

When you do this, you'll see K'=(v'/c, 1/lambda',0,0), once you substitute in what you got for v' and 1/lambda' in the previous part. You got the same values for these as I did, by the way so I think they are correct. I'm pretty sure this is all you have to do to show it transforms by LT. Someone please correct me if I'm wrong.