Webpage title: Calculating Distance Between Nodes in a Standing Wave on a String

[gleeman]

The question is: "Two traveling waves are superposed on the same string. Waves are y1=Asin (ωt−kx) and y2=Asin(ωt+kx).The distance between adjacent nodes of the resulting standing wave is: "

This is the question I have tried to solve.
I know that the distance between two nodes is 2pii. Then I do not know how to proceed.

The answer is pii/k,
but I do not know how it is obtained.

Please, do not hesitate to reply if you know why the answer is pii/k.

Thank you in advance!

 

[Snazzy]

-kx and +kx is the phase shift of the two waves. How far apart are the two waves then? How can you relate this to the period and the distance, x?

 

[gleeman]

Thank you, you solved this question as 2pii=2kx => Distance(x)=pii/k.