Question:
In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is \( t \) second. The frequency of vibration of air column is
In fundamental mode, the time required for the sound wave to reach upto the closed end of pipe filled with air is \( t \) second. The frequency of vibration of air column is
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For a closed pipe, the fundamental wavelength is \(4L\). The time to travel one length is \(L/v\). Use this to eliminate \(v\) and find \(f\) directly.
Updated On: Jun 1, 2026
- \(\frac{1}{t}\)
- \(\frac{2}{t}\)
- \(\frac{3}{t}\)
- \(\frac{0.25}{t}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
A closed pipe (closed at one end, open at the other) in its fundamental mode. The time for sound to travel from the open end to the closed end is \(t\). We need the frequency.
Step 2: Key Formula or Approach:
For a closed pipe, fundamental frequency \(f = \frac{v}{4L}\), where \(L\) is the length of the pipe. The time to travel from open end to closed end is \(t = \frac{L}{v}\) (distance \(L\), speed \(v\)). Thus \(v = L/t\).
Step 3: Detailed Explanation:
Substitute \(v = L/t\) into \(f = \frac{v}{4L}\): \[ f = \frac{L/t}{4L} = \frac{1}{4t} = \frac{0.25}{t}. \]
Step 4: Final Answer:
Frequency = \(\frac{0.25}{t}\), option (D).
A closed pipe (closed at one end, open at the other) in its fundamental mode. The time for sound to travel from the open end to the closed end is \(t\). We need the frequency.
Step 2: Key Formula or Approach:
For a closed pipe, fundamental frequency \(f = \frac{v}{4L}\), where \(L\) is the length of the pipe. The time to travel from open end to closed end is \(t = \frac{L}{v}\) (distance \(L\), speed \(v\)). Thus \(v = L/t\).
Step 3: Detailed Explanation:
Substitute \(v = L/t\) into \(f = \frac{v}{4L}\): \[ f = \frac{L/t}{4L} = \frac{1}{4t} = \frac{0.25}{t}. \]
Step 4: Final Answer:
Frequency = \(\frac{0.25}{t}\), option (D).
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