Q. No.An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is \(50~\text{cm}.\) The next larger length of the column resonating with the same tuning fork will be:
1.
\(100~\text{cm}\)
2.
\(150~\text{cm}\)
3.
\(200~\text{cm}\)
4.
\(66.7~\text{cm}\)
A uniform rope, of length \(L\) and mass \(m_1,\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2.\) The ratio \(\frac{\lambda_2}{\lambda_1}\) is:
| 1. | \(\sqrt{\dfrac{m_1+m_2}{m_2}}\) | 2. | \(\sqrt{\dfrac{m_2}{m_1}}\) |
| 3. | \(\sqrt{\dfrac{m_1+m_2}{m_1}}\) | 4. | \(\sqrt{\dfrac{m_1}{m_2}}\) |
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 |
| 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. |
A source of unknown frequency gives \(4\) beats/s when sounded with a source of known frequency of \(250~\text{Hz}.\) The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of \(513~\text{Hz}.\) The unknown frequency will be:
| 1. | \(246~\text{Hz}\) | 2. | \(240~\text{Hz}\) |
| 3. | \(260~\text{Hz}\) | 4. | \(254~\text{Hz}\) |
A wave traveling in the +ve \(x\text-\)direction having maximum displacement along \(y\text-\)direction as \(1~\text{m}\), wavelength \(2\pi~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
| 1. | \(y=\sin (2 \pi x-2 \pi t)\) | 2. | \(y=\sin (10 \pi x-20 \pi t)\) |
| 3. | \(y=\sin (2 \pi x+2 \pi t)\) | 4. | \( y=\sin (x-2 t)\) |
\(y_2 = a\cos(\omega t+kx)~\text{m},\) where \(x\) is in meters and \(t\) in seconds. The phase difference between them is:
1. \(1.25\) rad
2. \(1.57\) rad
3. \(0.57\) rad
4. \(1.0\) rad
| 1. | increase by a factor of \(20\). |
| 2. | increase by a factor of \(10\). |
| 3. | decrease by a factor of \(20\). |
| 4. | decrease by a factor of \(10\). |
1. \(y =(0.02~\text{m})\sin(7.85x+1005t)\)
2. \(y =(0.02~\text{m})\sin(15.7x-2010t)\)
3. \(y =(0.02~\text{m})\sin(15.7x+2010t)\)
4. \(y =(0.02~\text{m})\sin(7.85x-1005t)\)
| 1. | \(5\) | 2. | \(7\) |
| 3. | \(8\) | 4. | \(3\) |
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