MHT CET · Physics · Waves and Sound
An air column in a closed organ pipe vibrating in unison with a fork, produces second overtone. The vibrating air column has
- A three nodes and two antinodes.
- B three nodes and three antinodes.
- C four nodes and three antinodes.
- D three nodes and four antinodes.
Answer & Solution
Correct Answer
(B) three nodes and three antinodes.
Step-by-step Solution
Detailed explanation
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.
\(\mathrm{f}_{\mathrm{n}}=\frac{\mathrm{nV}}{4 \mathrm{~L}}\)
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.
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