Q. No.The equation of vibration of a taut string, fixed at both ends, is given by: \(y=(4~\text{mm})~\cos\left(\dfrac{\pi x}{30~\text{cm}}\right)~\sin\Big(400\pi s^{-1}t\Big) \)
At which points is the amplitude equal to \(2\) mm?
At which points is the amplitude equal to \(2\) mm?
| 1. | \(x = \) \(10\) cm, \(20\) cm, \(30\) cm, \(40\) cm |
| 2. | \(x=\) \(10\) cm, \(15\) cm, \(30\) cm, \(45\) cm |
| 3. | \(x =\) \(10\) cm, \(20\) cm, \(40\) cm, \(80\) cm |
| 4. | \(x = \) \(10\) cm, \(20\) cm, \(40\) cm, \(50\) cm |
Subtopic: Standing Waves |
Level 3: 35%-60%
Hints
A guitar string and an open organ pipe are set into vibration and they are observed to be in resonance. At resonance,
| 1. | the frequencies of the mechanical vibrations on the respective instruments are equal |
| 2. | the wavelengths of the mechanical vibrations on the respective instruments are equal |
| 3. | both the frequencies and wavelengths of the mechanical vibrations on the respective instruments are equal |
| 4. | either the frequencies or the wavelengths of the mechanical vibrations on the respective instruments are equal |
Subtopic: Standing Waves |
63%
Level 2: 60%+
Hints
At the closed end of a closed organ pipe vibrating in its fundamental mode:
| 1. | there is a pressure node, but a displacement antinode |
| 2. | there is a pressure antinode, but a displacement node |
| 3. | there are pressure and displacement nodes |
| 4. | there are pressure and displacement antinodes |
Subtopic: Standing Waves |
62%
Level 2: 60%+
Hints
The first overtone of a closed pipe has a frequency \(f_c.\) A frequency that is \(2f_c\) can be excited from an open pipe of the same length but vibrating in its:
| 1. | \(2^{\text{nd}}\) harmonic | 2. | \(3^{\text{rd}}\) harmonic |
| 3. | \(6^{\text{th}}\) harmonic | 4. | \(12^{\text{th}}\) harmonic |
Subtopic: Standing Waves |
68%
Level 2: 60%+
Hints
The first overtone of a closed organ pipe of length \(l_1\) matches the fundamental frequency of an open pipe of length \(l_2\). Then,
1. \(l_1 = 2l_2\)
2. \(l_2 = 2l_1\)
3. \(2l_1 = 3l_2\)
4. \(2l_2 = 3l_1\)
1. \(l_1 = 2l_2\)
2. \(l_2 = 2l_1\)
3. \(2l_1 = 3l_2\)
4. \(2l_2 = 3l_1\)
Subtopic: Standing Waves |
68%
Level 2: 60%+
Hints
A closed organ pipe of length \({\dfrac{1}{3}}~\text m\) vibrates in its \(1^{\text{st}}\) overtone (in air). The speed of sound, in air, is \({\dfrac{1}{3}}\times10^3~\text{m/s}.\) The frequency heard is:
1. \(1000~\text{Hz}\)
2. \(500~\text{Hz}\)
3. \(250~\text{Hz}\)
4. \(750~\text{Hz}\)
1. \(1000~\text{Hz}\)
2. \(500~\text{Hz}\)
3. \(250~\text{Hz}\)
4. \(750~\text{Hz}\)
Subtopic: Standing Waves |
67%
Level 2: 60%+
Hints
Two waveforms travelling along the \(x\)-axis are superposed: \(y_1(x,t)=2~\text{mm}\sin2\pi\big[(100~\text s^{-1})t+(10~\text m^{-1})x\big]\) and \(y_2(x,t)=2~\text{mm}\sin2\pi\big[(10~\text m^{-1})x-(100~\text s^{-1})t\big],\) and their superposition is \(y(x,t)=y_1+y_2.\) This represents:
| 1. | a \(100~\text{Hz}\) waveform travelling along positive \(x\) |
| 2. | a \(100~\text{Hz}\) waveform travelling along negative \(x\) |
| 3. | a \(100~\text{Hz}\) – standing waveform |
| 4. | a \(200~\text{Hz}\) – standing waveform |
Subtopic: Standing Waves |
67%
Level 2: 60%+
Hints
The fundamental frequencies of a closed pipe and an open pipe are identical. The first overtone for the closed pipe is \(f_c\) and for the open pipe is \(f_o.\) Their ratio \(\dfrac{f_c}{f_o}\) is:
| 1. | \(1\) | 2. | \(1/2\) |
| 3. | \(2/3\) | 4. | \(3/2\) |
Subtopic: Standing Waves |
70%
Level 2: 60%+
Hints
Two organ pipes – an open one of length \(L_1\) and a closed one of length \(L_2\) are set into vibration and it is observed that they resonate with each other in their fundamental modes. Then, \(\Large\frac{L_1}{L_2}\) equals:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\Large\frac12\) | 4. | \(\Large\frac14\) |
Subtopic: Standing Waves |
70%
Level 2: 60%+
Hints
A \(100\) cm wire of mass \(40\) g is fixed at both ends. A tuning fork, vibrating at a frequency of \(50\) Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is:
| 1. | \(400\) N | 2. | \(100\) N |
| 3. | \(25\) N | 4. | \(1600\) N |
Subtopic: Standing Waves |
75%
Level 2: 60%+
Hints
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