A tube, closed at one end and containing air, produces, when...

A tube, closed at one end and containing air, produces, when excited, the fundamental note of frequency $512 \mathrm{~Hz}$. If the tube is opened at both ends what is the fundamental frequency that can be excited (in $\mathrm{Hz}$ )?
(A) 256
(B) 1024
(C) 128
(D) 512

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Key Concepts

Fundamental Frequency Calculation

The fundamental frequency of a resonating tube is determined by the relation between the speed of sound, the wavelength, and the physical length of the tube. Given the different wavelength conditions imposed by the boundary conditions in open and closed tubes, changing the configuration of the tube alters the fundamental frequency that can be excited.

Standing Waves in Air Columns

Standing waves form when waves reflect in a medium like an air column and interfere with themselves, creating patterns of nodes (points of no motion) and antinodes (points of maximum motion). The formation of these standing waves depends on the boundary conditions at the ends of the tube, which dictate the specific positions of the nodes and antinodes.

Resonance in Open and Closed Tubes

The resonance conditions differ between tubes that are open at both ends and those that are closed at one end. A tube closed at one end will have a node at the closed end and an antinode at the open end, resulting in a fundamental wavelength that is four times the length of the tube. In contrast, a tube that is open at both ends will have antinodes at both ends, and its fundamental wavelength is twice the length of the tube.

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