QUESTION ABOUT REDSHIFT:

So I understand the concept of redshift, in that objects traveling away causes their light waves to become stretched, forcing it lower into the electromagnetic spectrum, making it appear 'red'. So does this mean that all waves have a constant 'length' if you will? As in, are waves sort of like a 'string,' in that as they become longer, the total 'length' must remain constant by the height of their amplitudes diminishing?

I hope that was understandable, I'm having a hard time figuring out how to even word the question.