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Strings fixed at both ends and open pipes (antinodes at both ends) share the same harmonic structure: all harmonics are present. Fundamental frequency $f_1 = v/(2L)$, with overtones at $2f_1, 3f_1, 4f_1, ...$. The $n$th harmonic has $n$ loops (for strings) or $n$ displacement antinodes.

For strings, $v = \sqrt{T/\mu}$, so $f_1 = (1/(2L))\sqrt{T/\mu}$. The three laws of vibrating strings follow: $f \propto 1/L$ (inverse length), $f \propto \sqrt{T}$ (square root of tension), and $f \propto 1/\sqrt{\mu}$ (inverse square root of mass per length). Sonometer experiments verify these laws. When a string is plucked at position $L/n$ from one end, the $n$th harmonic (and its multiples) are suppressed because a node is forced at the plucking point.

For open pipes, $v$ is the speed of sound, and end correction $e \approx 0.6r$ extends the effective length by $2e$ (one correction at each open end). The quality (timbre) of an open pipe is richer than a closed pipe because all harmonics contribute to the sound, producing a fuller tone.