gen-define-open-versus-closed-pipes-and-give-one-short-worked-ex-1388

Define open versus closed pipes and give one short worked example.

# Open vs Closed Pipes ## Definitions **Closed Pipe (Stopped Pipe):** - Closed at one end, open at the other - Supports only **odd harmonics** (1st, 3rd, 5th, ...) - Closed end = displacement node (pressure antinode) - Open end = displacement antinode (pressure node) - Fundamental frequency: **f₁ = v/4L** **Open Pipe:** - Open at both ends - Supports **all harmonics** (1st, 2nd, 3rd, ...) - Both ends = displacement antinodes - Fundamental frequency: **f₁ = v/2L** ## Worked Example **Problem:** A pipe is 0.85 m long. Find the fundamental frequency if it's (a) open at both ends, (b) closed at one end. (Use v = 340 m/s) **Solution:** **(a) Open pipe:** - f₁ = v/2L = 340/(2 × 0.85) = 340/1.7 = **200 Hz** **(b) Closed pipe:** - f₁ = v/4L = 340/(4 × 0.85) = 340/3.4 = **100 Hz** **Note:** The closed pipe has half the fundamental frequency (sounds one octave lower) than the same length open pipe.