The superposition of two traveling waves of the same frequency (with the same polarization and amplitude) traveling in the opposite directions results in standing waves. Typically, a travelling wave and its reflection are used to accomplish this, guaranteeing that the frequency will always be the same.
A wave that is moving along the string in one direction reflects off the end and comes back inverted because the end is fixed. This produces exactly the two identical waves that are required for a standing wave to travel on the string in opposite directions.
When two waves with the same frequency and amplitude move in opposition to one another and interfere with one another, a standing wave results.
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