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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?
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 |
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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 |
 62%
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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%
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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 |
 67%
From NCERT

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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. \(2l_2 = 3l_1\)
Subtopic:  Standing Waves |
 67%
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A closed organ pipe of length \({\large\frac{1}{3}}~\text m\) vibrates in its \(1^{\text{st}}\) overtone (in air). The speed of sound, in air, is \({\large\frac{1}{3}}\times10^3~\text{m/s}.\) The frequency heard is:
1. \(1000~\text{Hz}\) 2. \(500~\text{Hz}\)
3. \(250~\text{Hz}\) 4. \(750~\text{Hz}\)
Subtopic:  Standing Waves |
 66%
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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%
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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%
From NCERT

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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%

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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 |
 74%
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