Question:
A pipe open at both ends has length \(1\) m. The air column in a pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air \(=340\) m/s)
A pipe open at both ends has length \(1\) m. The air column in a pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air \(=340\) m/s)
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An open pipe resonates at all integral multiples of v divided by 2L.
Updated On: Nov 12, 2026
- \(510\) Hz
- \(340\) Hz
- \(170\) Hz
- \(85\) Hz
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
For a pipe open at both ends, \(f_{n}=\dfrac{nv}{2L}\) with \(n=1,2,3,\dots\).
Step 2: Fundamental
\(f_{1}=\dfrac{340}{2\times1}=170\) Hz.
Step 3: Allowed values
The resonant frequencies are 170, 340, 510, ... Hz. Hence 85 Hz is not a multiple of 170 Hz.
Final Answer:
The air column cannot resonate at 85 Hz. \[ \boxed{\text{(D) }85\ \text{Hz}} \]
For a pipe open at both ends, \(f_{n}=\dfrac{nv}{2L}\) with \(n=1,2,3,\dots\).
Step 2: Fundamental
\(f_{1}=\dfrac{340}{2\times1}=170\) Hz.
Step 3: Allowed values
The resonant frequencies are 170, 340, 510, ... Hz. Hence 85 Hz is not a multiple of 170 Hz.
Final Answer:
The air column cannot resonate at 85 Hz. \[ \boxed{\text{(D) }85\ \text{Hz}} \]
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