Question:
An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency 415 Hz for various vibrating air columns. Which one of the following lengths is not in resonance ? (velocity of sound in air = 332 m/s) (Neglect end correction)
An air column in a pipe which is closed at one end will be in resonance with a vibrating tuning fork of frequency 415 Hz for various vibrating air columns. Which one of the following lengths is not in resonance ? (velocity of sound in air = 332 m/s) (Neglect end correction)
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A closed pipe resonates at odd multiples of a quarter wavelength.
Updated On: Oct 1, 2026
- \(20 \text{cm}\)
- \(40 \text{cm}\)
- \(60 \text{cm}\)
- \(100 \text{cm}\)
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The Correct Option is B
Solution and Explanation
Step 1: Wavelength
\(\lambda = \frac vf = \frac{332}{415} = 0.8\ \text{m}\), so \(\frac\lambda4 = 20\ \text{cm}\).
Step 2: Condition
Resonance in a closed pipe needs \(l = (2n+1)\frac\lambda4\), so \(l = 20, 60, 100, 140\ \text{cm}\ldots\).
Step 3: Compare
\(20\), \(60\) and \(100\) cm are odd multiples of \(20\). \(40 cm\) is an even multiple, so it is not in resonance. Option (B).
Final Answer:
40 cm is not in resonance. \[ \boxed{\text{(B)}\ 40\ \text{cm}} \]
\(\lambda = \frac vf = \frac{332}{415} = 0.8\ \text{m}\), so \(\frac\lambda4 = 20\ \text{cm}\).
Step 2: Condition
Resonance in a closed pipe needs \(l = (2n+1)\frac\lambda4\), so \(l = 20, 60, 100, 140\ \text{cm}\ldots\).
Step 3: Compare
\(20\), \(60\) and \(100\) cm are odd multiples of \(20\). \(40 cm\) is an even multiple, so it is not in resonance. Option (B).
Final Answer:
40 cm is not in resonance. \[ \boxed{\text{(B)}\ 40\ \text{cm}} \]
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