If the C were played on an organ pipe that was open at one...

If the $C$ were played on an organ pipe that was open at one end and closed at the other, which of the harmonic frequencies in Figure P16.72 would be present? A. All of the harmonics in the figure would be present. B. $262,786,$ and $1310 \mathrm{Hz}$ $\mathrm{C} .524,1048,$ and $1572 \mathrm{Hz}$ D. $262,524,$ and $1048 \mathrm{Hz}$

If the $C$ were played on an organ pipe that was open at one end and closed at the other, which of the harmonic frequencies in Figure P16.72 would be present?
A. All of the harmonics in the figure would be present.
B. $262,786,$ and $1310 \mathrm{Hz}$
$\mathrm{C} .524,1048,$ and $1572 \mathrm{Hz}$
D. $262,524,$ and $1048 \mathrm{Hz}$

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Key Concepts

Boundary Conditions in Open-Closed Pipes

In an organ pipe that is open at one end and closed at the other, the boundary conditions force a displacement node at the closed end and a displacement antinode at the open end. These conditions restrict the allowed standing wave modes to those with a quarter-wavelength fitting into the pipe for the fundamental frequency, and only odd multiples of this quarter-wavelength for overtones. This results in the presence of only odd harmonics in such pipes.

Harmonics

Harmonics are frequencies that are integer multiples of a fundamental frequency. They represent the different modes in which a system can naturally oscillate. In musical acoustics, the harmonic series gives rise to the overtones that, combined with the fundamental frequency, determine the timbre or color of the sound produced.

Standing Waves in Pipes

Standing waves form when waves reflect off the boundaries of a medium and interfere with incoming waves, creating a pattern of nodes and antinodes. In pipes, standing waves dictate which frequencies, or harmonics, will be reinforced. The pattern of nodes and antinodes depends on the type of boundary at the ends of the pipe.

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