How does the recapitulation create a sense of resolution in sonata form?

The recapitulation creates a sense of resolution in sonata form by serving as a final synthesis that reconciles the musical conflicts established earlier in the movement.1

While the exposition introduces themes in contrasting keys—typically moving from the tonic to the dominant—the recapitulation restates these subjects with both themes anchored in the tonic key. This shift provides a new state of equilibrium, resolving the tonal tension that defined the earlier sections.1

By returning to the original key, the recapitulation allows the listener to perceive the previously conflicting subjects in a unified relationship, similar to a traveler who, after viewing parts of a landscape separately, finally sees the entire scene as a whole from a summit. This process effectively brings about the reconciliation of opposites, which is essential to the structure of sonata form. If these conflicts remain unresolved, a coda may be added to further round off the movement.1