What changes when a wave move from 1 string to another.

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I want to know if wave length or frequency will change when a wave move from a string of a certain linear density to another of a different linear density?
 
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When you say it moves to the other string, do you mean vibrations in the second arising because of the movement of the first? Or are you merely replacing one string with another and applying the same stimulus?
 
I mean two strings are attached or 1 string with varying density. The wave then travel from one part to another.
 
OK, so it's a traveling wave. That means some source is generating the wave at one end. Where the wave hits the boundary, what will the frequency be at that point? How will that relate to the frequency each side?