First three normal modes for a string ended with two perfect boundaries. Two fixed boundaries (left) lead to standing waves that end with nodes on both sides, while two free boundaries (middle) lead to standing waves that end with antinodes on both sides. A combination of different boundaries (right) leads to standing waves that end with one node and one antinode. Normal modes appear only for very particular relations between inter-border distance L, wavelength λ and therefore frequency f.

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