Standing Wave Nodes and Interference on a Stretched String

[RUphysics3]

Homework Statement

Two sinusodial waves, each of wavelength 5m and amplitude 10cm, travel in opposite directions on a 20m streched string which is clamped at each end. Excluding the nodes at the ends , how many nodes appear in the resulting standing wave?

Homework Equations

The Attempt at a Solution

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So I just drew a picture, 20m long string, and drew a wave through it with each wavelength being 5m. I basically disregarded that there were two separate waves. I still got the right answer. Is the fact that they collide irrelevant? Why?

 

[haruspex]

So I just drew a picture, 20m long string, and drew a wave through it with each wavelength being 5m. I basically disregarded that there were two separate waves. I still got the right answer. Is the fact that they collide irrelevant? Why?

It is only irrelevant once proved to be so.
Consider an instant at which the two waves reinforce to the maximum extent at some point. Drawa picture of this. Draw the two individual waves on the same picture. Do they reinforce everywhere at that time? Compare the nodes of the three waves.