Q. No.Given the equation of a travelling wave in a string is \(y=0.04\sin(4x-2t),\) where \(y\) and \(x\) are in metre and \(t\) is in seconds. The equation for the velocity of oscillation of particle of string at \(x = x_{0},\) is:
1. \(0.16 \cos(4x_0-2t)\)
2. \(-0.16 \sin(4x_0-2t)\)
3. \(0.04 \cos(4x_0-2t)\)
4. \(-0.08\cos(4x_0-2t)\)
1. \(0.16 \cos(4x_0-2t)\)
2. \(-0.16 \sin(4x_0-2t)\)
3. \(0.04 \cos(4x_0-2t)\)
4. \(-0.08\cos(4x_0-2t)\)
Subtopic: Travelling Wave on String |
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A wave travelling along a string is described by, \(y(x,t)=0.005 \text{ sin}(80.0x-3.0t),\) in which the numerical constants are in SI units. The wavelength and the period of the wave respectively are:
1. \(7.85\) cm and \(2.09\) s
2. \(7.85\) mm and \(1.09\) s
3. \(7.85\) m and \(0.09\) s
4. none of these
Subtopic: Travelling Wave on String |
76%
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A wave travelling along a string is described by, \(y(x,~t)=0.005 ~\sin(80.0x-3.0t),\) in which the numerical constants are in SI units. The displacement \(y\) of the wave at a distance \(x = 30.0\) cm and time \(t=20\) s is:
1. \(0.5\) mm
2. \(5\) mm
3. \(5\) m
4. \(5\) cm
Subtopic: Travelling Wave on String |
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From NCERT
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If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
1. \(1:2\)
2. \(1:1\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{2}\)
1. \(1:2\)
2. \(1:1\)
3. \(\sqrt{2}:1\)
4. \(1:\sqrt{2}\)
Subtopic: Travelling Wave on String |
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A heavy uniform rope is suspended from the ceiling, and a block equal to \(3\) times the mass of the rope is suspended from the bottom. The ratio of the speed of a transverse pulse at the top \((v_t)\) to its speed at the bottom \((v_b)\) of the rope, \(\dfrac{v_t}{v_b}=\)
| 1. | \(\dfrac43\) | 2. | \(\sqrt{\dfrac43}\) |
| 3. | \(\dfrac34\) | 4. | \(\sqrt{\dfrac34}\) |
Subtopic: Travelling Wave on String |
77%
From NCERT
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A metallic wire with mass per unit length \(6\times 10^{-3}\) kg/m is under the tension of \(60\) N. What is the speed of transverse wave in the wire?
| 1. | \(100\) m/s | 2. | \(500\) m/s |
| 3. | \(600\) m/s | 4. | \(10,000\) m/s |
Subtopic: Travelling Wave on String |
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A string with a mass \(2.50~\text{kg}\) is under a tension of \(200~\text{N}\). The length of the stretched string is \(20.0~\text{m}\). If the transverse jerk is struck at one end of the string, how long does it take for the disturbance to reach the other end?
| 1. | \(0.5~\text{s}\) | 2. | \(0.6~\text{s}\) |
| 3. | \(0.4~\text{s}\) | 4. | \(0.1~\text{s}\) |
Subtopic: Travelling Wave on String |
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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 |
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A string of length \(1\) m and mass per unit length \(0.001\) kg/m is hanging vertically as shown. A small pulse is generated at its lower end. The pulse reaches the top end in approximately: (Take \(g=10\) m/s2)
| 1. | \({\dfrac 1 {\sqrt {10}}}\) s | 2. | \({\dfrac 3 { \sqrt {10}}} \) s |
| 3. | \( {\sqrt{\dfrac{2}{5}}} \) s | 4. | \(\dfrac {\sqrt {5}} 2\) s |
Subtopic: Travelling Wave on String |
From NCERT
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A steel wire \(0.72~\text{m}\) long has a mass of \(5\times10^{-3}~\text{kg}\). If the wire is under tension of \(60~\text{N}\), the speed of transverse waves on the wire will be:
1. \(85~\text{m/s}\)
2. \(83~\text{m/s}\)
3. \(93~\text{m/s}\)
4. \(100~\text{m/s}\)
Subtopic: Travelling Wave on String |
72%
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