MHT CET · Physics · Waves and Sound
An air column in a pipe, which is closed at one end will be in resonance with a vibrating tuning fork of frequency \(264 \mathrm{~Hz}\) for various lengths. Which one of the following lengths is not possible? \((\mathrm{V}=330 \mathrm{~m} / \mathrm{s})\)
- A \(62.50 \mathrm{~cm}\)
- B \(93.75 \mathrm{~cm}\)
- C \(156.25 \mathrm{~cm}\)
- D \(31.25 \mathrm{~cm}\)
Answer & Solution
Correct Answer
(A) \(62.50 \mathrm{~cm}\)
Step-by-step Solution
Detailed explanation
\(
\mathrm{n}=264 \mathrm{~Hz}, \mathrm{~V}=300 \mathrm{~m} / \mathrm{s}
\)
For fundamental frequency, \(\mathrm{n}=\frac{\mathrm{V}}{4 \ell}\)
\(
\ell=\frac{\mathrm{V}}{4 \mathrm{n}}=\frac{330}{4 \times 264}=0.3125 \mathrm{n}=31.25 \mathrm{~cm}
\)
For fundamental mode, \(\ell=\frac{\lambda}{4}\) other possible lengths are \(\frac{3 \lambda}{4}, \frac{5 \lambda}{4}, \ldots \ldots\) Hence, \(62.50 \mathrm{~m}\) is not possible.
\mathrm{n}=264 \mathrm{~Hz}, \mathrm{~V}=300 \mathrm{~m} / \mathrm{s}
\)
For fundamental frequency, \(\mathrm{n}=\frac{\mathrm{V}}{4 \ell}\)
\(
\ell=\frac{\mathrm{V}}{4 \mathrm{n}}=\frac{330}{4 \times 264}=0.3125 \mathrm{n}=31.25 \mathrm{~cm}
\)
For fundamental mode, \(\ell=\frac{\lambda}{4}\) other possible lengths are \(\frac{3 \lambda}{4}, \frac{5 \lambda}{4}, \ldots \ldots\) Hence, \(62.50 \mathrm{~m}\) is not possible.
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