A closed organ pipe has fundamental frequency 100 Hz. What frequencies will be produced if its

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A closed organ pipe has fundamental frequency 100 Hz. What...

A closed organ pipe has fundamental frequency $100 \mathrm{~Hz}$. What frequencies will be produced if its other end is also opened?
(A) $200,400,600,800 \ldots \ldots$
(B) $200,300,400,500 \ldots \ldots$
(C) $100,300,500,700 \ldots \ldots$
(D) $100,200,300,400 \ldots \ldots$

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Key Concepts

Harmonic Series

The harmonic series in tubes refers to the set of frequencies at which the pipe resonates. For a pipe with both ends open, all integer multiples of the fundamental frequency are present. In contrast, a pipe with one end closed supports only odd multiples of the fundamental frequency. This distinction explains how modifying the boundary conditions alters the predicted frequency pattern at which the pipe vibrates.

Standing Waves in Pipes

Standing waves form in pipes when sound waves reflect off the ends and interfere with each other, creating points of no vibration (nodes) and maximum vibration (antinodes). The pattern of these standing waves depends on the conditions at the ends of the pipe, which determine how the wave reflects and what modes of vibration are permitted.

Boundary Conditions at Pipe Ends

The behavior of sound waves in a pipe is critically influenced by its boundary conditions. An open end of a pipe acts as an antinode because the air is free to oscillate, while a closed end acts as a node because the air is forced to remain still. Changing whether an end is open or closed alters the positions of nodes and antinodes, thus changing the resonant frequencies of the pipe.

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