A speaker and frequency generator are used to create resonances in two pipes. Pipe A of length L is open at both ends. Pipe B is also of length L but is closed at one end. Which statement about the fundamental frequencies produced by the pipes is true?A.The fundamental frequency of pipe A will be twice as great as the fundamental frequency of B, because antinodes must occur at open ends and nodes must occur at closed ends.B.The fundamental frequency of pipe A will be half as great as the fundamental frequency of B, because antinodes must occur at open ends and nodes must occur at closed ends.C.The fundamental frequencies of the pipes are the same, because the speed of sound is the same in both pipes.D.The fundamental frequencies of the pipes are the same, because all pipes of equal length will resonate at the same frequency.
Question
A speaker and frequency generator are used to create resonances in two pipes. Pipe A of length L is open at both ends. Pipe B is also of length L but is closed at one end. Which statement about the fundamental frequencies produced by the pipes is true?A.The fundamental frequency of pipe A will be twice as great as the fundamental frequency of B, because antinodes must occur at open ends and nodes must occur at closed ends.B.The fundamental frequency of pipe A will be half as great as the fundamental frequency of B, because antinodes must occur at open ends and nodes must occur at closed ends.C.The fundamental frequencies of the pipes are the same, because the speed of sound is the same in both pipes.D.The fundamental frequencies of the pipes are the same, because all pipes of equal length will resonate at the same frequency.
Solution
The correct answer is A. The fundamental frequency of pipe A will be twice as great as the fundamental frequency of B, because antinodes must occur at open ends and nodes must occur at closed ends.
Here's why:
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The fundamental frequency, also known as the first harmonic, is the lowest frequency of a resonance system.
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In a pipe that is open at both ends (like pipe A), the fundamental frequency occurs when there is an antinode (a point of maximum vibration) at each end and a node (a point of minimum vibration) in the middle. This is equivalent to half a wavelength fitting inside the pipe.
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In a pipe that is closed at one end (like pipe B), the fundamental frequency occurs when there is a node at the closed end and an antinode at the open end. This is equivalent to a quarter of a wavelength fitting inside the pipe.
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Therefore, for pipes of the same length, the fundamental frequency of the pipe open at both ends will be twice as great as the fundamental frequency of the pipe closed at one end. This is because twice as much of the wave fits inside the open pipe compared to the closed pipe.
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