| 1. | \( 155~\text{Hz} \) | 2. | \( 205~\text{Hz} \) |
| 3. | \( 10.5~\text{Hz} \) | 4. | \( 105~\text{Hz} \) |
The fundamental frequency of a closed organ pipe of a length \(20\) cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:
| 1. | \(80\) cm | 2. | \(100\) cm |
| 3. | \(120\) cm | 4. | \(140\) cm |
If \(n_1\), \(n_2\), and \(n_3\) are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency \(n\) of the string is given by:
| 1. | \( \frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\) |
| 2. | \( \frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}\) |
| 3. | \( \sqrt{n}=\sqrt{n_1}+\sqrt{n_2}+\sqrt{n_3}\) |
| 4. | \( n=n_1+n_2+n_3\) |
The number of possible natural oscillations of the air column in a pipe closed at one end of length \(85\) cm whose frequencies lie below \(1250\) Hz are:
(velocity of sound= \(340~\text{m/s}\)
| 1. | \(4\) | 2. | \(5\) |
| 3. | \(7\) | 4. | \(6\) |
| 1. | Odd harmonics of the fundamental frequency will be generated. |
| 2. | All harmonics of the fundamental frequency will be generated. |
| 3. | Pressure change will be maximum at both ends. |
| 4. | The open end will be an antinode. |
| 1. | \(\dfrac{1500}{23} \mathrm{~cm}, \dfrac{500}{23} \mathrm{~cm} \) |
| 2. | \(\dfrac{1500}{23} \mathrm{~cm}, \dfrac{300}{23} \mathrm{~cm} \) |
| 3. | \(\dfrac{300}{23} \mathrm{~cm}, \dfrac{1500}{23} \mathrm{~cm} \) |
| 4. | \(\dfrac{1500}{23} \mathrm{~cm}, \dfrac{2000}{23} \mathrm{~cm}\) |