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Q. No.
A string \((AB)\) under tension has a fundamental frequency of \(120~\text{Hz}.\) The string is set into vibration and a point \(P\) is held down by a finger so that it becomes a node (i.e., \(P\) does not vibrate):\(\Large\frac{AP}{PB}=\frac12.\) The lowest frequency for which this happens is:

           
1. \(120~\text{Hz}\)
2. \(240~\text{Hz}\)
3. \(360~\text{Hz}\)
4. \(180~\text{Hz}\)
Subtopic:  Travelling Wave on String |
Level 3: 35%-60%

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A string fixed at both ends is under tension \(T.\) It has a length \(L,\) and mass \(m.\) The fundamental frequency of the vibration is: 
1. \(\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}\) 2. \(\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}\)
3. \(\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}\) 4. \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\)
Subtopic:  Travelling Wave on String |
 58%
Level 3: 35%-60%

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A heavy uniform rope \(PQ\) is suspended from the ceiling. The lowest end of the rope is given a sharp transverse "shake" (or vibration) so as to cause a pulse. This pulse travels upward. As it travels upward, its speed:
1. increases 2. decreases
3. first increases and then decreases 4. remains constant
Subtopic:  Travelling Wave on String |
 58%
Level 3: 35%-60%

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The speed of elastic waves on a stretched string under tension is \(u.\) The tension in the string is increased by \(1\%.\) The speed of elastic waves will become (nearly):
1. \(u+\dfrac{u}{100}\) 2. \(u-\dfrac{u}{100}\)
3. \(u+\dfrac{u}{200}\) 4. \(u-\dfrac{u}{200}\)
Subtopic:  Travelling Wave on String |
 61%
Level 2: 60%+

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The first overtone of a string \((A)\) fixed at both ends is in resonance with the second overtone of a similar string \((B),\) also fixed at both ends. Both strings are under the same tension and have the same mass per unit length. Their respective lengths are \(L_A\) and \(L_B.\) Then:
1. \(L_A=2L_B\)     2. \(L_A=\Large{\frac{L_B}{2}}\)    
3. \(2L_A=3L_B\) 4. \(\Large{\frac{L_A}{2}=\frac{L_B}{3}}\)
Subtopic:  Travelling Wave on String |
 66%
Level 2: 60%+

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A rope of uniform mass per unit length \(\mu\) is suspended from the ceiling, hanging under its own weight. If a small transverse pulse is formed at its lower end \(A\), it travels upward with a local speed \(v=\sqrt {\dfrac{\text{tension}}{\text{mass/length}}}\).
                         
The speed of the pulse is:
1. maximum at \(A,\) minimum at \(O\)
2. minimum at \(A,\) maximum at \(O\)
3. uniform
4. minimum at \(A\) and \(O,\) maximum in the middle
Subtopic:  Travelling Wave on String |
 72%
Level 2: 60%+

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A wave-pulse moves along a string and gets reflected from the fixed end \(A.\) After the pulse has been reflected, the displacement is given by:
1.
2.
3.
4.
Subtopic:  Travelling Wave on String |
 75%
Level 2: 60%+

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