Part of JWAVE-02 — Waves: Standing Waves, Beats & Doppler Effect

Closed Pipe Harmonics — Only Odd

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Closed pipe: node at closed end, antinode at open end. L=(2n1)λ/4L = (2n-1)\lambda/4 for n=1,2,3,...n = 1, 2, 3, .... Frequencies: fn=(2n1)v/(4L)f_n = (2n-1)v/(4L). Only odd harmonics: f1=v/(4L)f_1 = v/(4L), 3f13f_1, 5f15f_1, ... The fundamental is half that of an open pipe of the same length. The missing even harmonics give the closed pipe a "hollow" or "dull" sound quality. First overtone of closed pipe (3f13f_1) is the 3rd harmonic, NOT the 2nd.

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