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

End Correction

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The antinode at an open end does not form exactly at the end — it forms slightly outside at distance e0.6re \approx 0.6r (where rr is the pipe radius). Effective length: closed pipe Leff=L+eL_{\text{eff}} = L + e; open pipe Leff=L+2eL_{\text{eff}} = L + 2e. In resonance tube experiments, using two consecutive resonance lengths eliminates ee: λ/2=L2L1\lambda/2 = L_2 - L_1 (independent of end correction). End correction: e=(L23L1)/2e = (L_2 - 3L_1)/2.

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