Maximum displacement when two waves with different amplitudes superpose

[Toon]

Homework Statement

"
Two traveling waves are generated on the same taut string. Individually, the two traveling waves can be described by the following two equations:

If both of the above traveling waves exist on the string at the same time, what is the maximum positive displacement that a point on the string can ever have?
3. At first I thought this problem was pretty straighfoward with just adding the two waves together. However my plan was to add them such that the outcome would be something like 2Asin(a+b)/2 * cos(a-b)/2
however the waves in the problem have diffrent amplitudes and I am not sure had to add them now. Any help would be appreciated, thanks!

 

[RUber]

Do you need to find a complicated answer using your k and phi terms?
Is it not reasonable to assume that regardless of the terms, there is a max that the sine function will take?

 

[andrewkirk]

Are the two waves traveling in the same, or in opposite directions?

Can a pair of peaks - one from each wave - ever coincide?

 

[phys1420]

add the two amplitudes to find the max superposition