An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The…

An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column has
  1. three nodes and two antinodes.
  2. three nodes and three antinodes.
  3. four nodes and three antinodes.
  4. three nodes and four antinodes.

Solution

Frequency of $\mathrm{n}^{\text {th }}$ harmonic of a closed pipe $\mathrm{f}_{\mathrm{n}}=\frac{\mathrm{nV}}{4 \mathrm{~L}}$
Frequency of different modes of vibration in a closed pipe $\mathrm{f}_{\mathrm{n}}^{\prime}=\frac{(2 n-1) \mathrm{V}}{4 \mathrm{~L}_1}$ $\therefore \quad$ Frequency of $2^{\text {nd }}$ overtone, $\mathrm{f}_3^{\prime}=\frac{5 \mathrm{~V}}{4 \mathrm{~L}_1}(\mathrm{n}=3)$ In a closed pipe, the number of nodes and antinodes are the same. Hence, there will be 3 nodes and 3 antinodes.

Asked in: MHT CET 2024 (02 May Shift 1)

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