Question:
An open organ pipe of length $L$ resonates at its fundamental frequency. The wavelength of the sound wave produced is
An open organ pipe of length $L$ resonates at its fundamental frequency. The wavelength of the sound wave produced is
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Remember for open pipes: The fundamental frequency's wavelength is twice the length of the pipe.
Updated On: Jun 3, 2026
- $2L$
- $L$
- $4L$
- $L/2$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
In an open organ pipe, the fundamental frequency corresponds to a standing wave pattern where both ends of the pipe are antinodes. The length of the pipe $L$ is equal to one-half of the wavelength $\lambda$ because there is no node at either end.
Step 2: Meaning
The question asks for the wavelength $\lambda$ of the sound wave produced by an open organ pipe that resonates at its fundamental frequency, given the length $L$ of the pipe.
Step 3: Analysis
For an open organ pipe: The fundamental mode has a single antinode in the middle and nodes at both ends. This means the distance between two consecutive nodes (or antinodes) is equal to one wavelength $\lambda$. Since the length $L$ of the pipe spans from one node to another, it is half of the wavelength. Therefore: \[L = \frac{\lambda}{2}\] Solving for $\lambda$, we get: \[\lambda = 2L\] This confirms that option A) $2L$ is the correct answer.
Step 4: Conclusion
The length $L$ of an open organ pipe corresponds to half a wavelength at its fundamental frequency. Thus, the full wavelength is twice this length.
Final Answer: (A)
In an open organ pipe, the fundamental frequency corresponds to a standing wave pattern where both ends of the pipe are antinodes. The length of the pipe $L$ is equal to one-half of the wavelength $\lambda$ because there is no node at either end.
Step 2: Meaning
The question asks for the wavelength $\lambda$ of the sound wave produced by an open organ pipe that resonates at its fundamental frequency, given the length $L$ of the pipe.
Step 3: Analysis
For an open organ pipe: The fundamental mode has a single antinode in the middle and nodes at both ends. This means the distance between two consecutive nodes (or antinodes) is equal to one wavelength $\lambda$. Since the length $L$ of the pipe spans from one node to another, it is half of the wavelength. Therefore: \[L = \frac{\lambda}{2}\] Solving for $\lambda$, we get: \[\lambda = 2L\] This confirms that option A) $2L$ is the correct answer.
Step 4: Conclusion
The length $L$ of an open organ pipe corresponds to half a wavelength at its fundamental frequency. Thus, the full wavelength is twice this length.
Final Answer: (A)
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