String & Pipe Closed Both Ends (Node–Node)
BINAS 35B2Tsokos Ch. 11.4
Overview
Both ends are fixed → both ends must be nodes. Harmonics: n = 1, 2, 3... (all harmonics present). Wavelength: λ_n = 2L/n. Frequency: f_n = nv/2L. The fundamental (n=1) has λ = 2L. Second harmonic (n=2) has λ = L. Same formulas apply to a pipe closed at BOTH ends (antinode-antinode would be open pipe — see next subtopic).