Any string shape decomposes into a combination of normal modes

Evidence

The two modes, in various combinations differing in the amplitude of each mode and their relative phase, can describe any initial shape for two beads that is possible. — Eric J. Heller, Why You Hear What You Hear- An…, 787

Categorization

• DEFINE: Explains the normal-mode decomposition concept: any plucked shape equals a unique combination of pure modes with set amplitudes and phases.
• XREF: Connects directly to Fourier / modal decomposition used throughout acoustics; parallels the standing-wave superpositions chapter.