Superposition: Adding two waves together amplitude help

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1. Sep 12, 2015

Toon

1. The problem statement, all variables and given/known data
"
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 im not sure had to add them now. Any help would be appreciated, thanks!

2. Sep 12, 2015

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?

3. Sep 12, 2015

andrewkirk

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

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