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Q. No.If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:
| 1. | the pulse is traveling along the negative \(x\text-\)axis. |
| 2. | the speed of the pulse is \(4\) m/s. |
| 3. | the amplitude of the pulse is \(5\) m. |
| 4. | all of these. |
Subtopic: Wave Motion |
85%
Level 1: 80%+
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For the travelling harmonic wave, \(y(x,t) = 2.0\cos 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:
1. \(0.8 \pi~\text{rad}\)
2. \(\pi~ \text{rad}\)
3. \(6.4\pi~\text{rad}\)
4. \(4\pi~\text{rad}\)
1. \(0.8 \pi~\text{rad}\)
2. \(\pi~ \text{rad}\)
3. \(6.4\pi~\text{rad}\)
4. \(4\pi~\text{rad}\)
Subtopic: Wave Motion |
68%
Level 2: 60%+
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The phase difference between two waves, represented by
\(y_1= 10^{-6}\sin \left\{100t+\left(\frac{x}{50}\right) +0.5\right\}~\text{m}\)
\(y_2= 10^{-6}\cos \left\{100t+\left(\frac{x}{50}\right) \right\}~\text{m}\)
where \(x\) is expressed in metres and \(t\) is expressed in seconds, is approximate:
1. \(2.07~\text{radians}\)
2. \(0.5~\text{radians}\)
3. \(1.5~\text{radians}\)
4. \(1.07~\text{radians}\)
Subtopic: Wave Motion |
65%
Level 2: 60%+
AIPMT - 2004
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The equation of a travelling wave is given as \(y = A\sin(40\pi t-0.2\pi x),\) where \(t\) is in seconds and \(x\) in metres. The minimum distance between two particles oscillating in the same phase is:
1. \(10~\text{m}\)
2. \(5~\text{m}\)
3. \(2~\text{m}\)
4. \(1.5~\text{m}\)
1. \(10~\text{m}\)
2. \(5~\text{m}\)
3. \(2~\text{m}\)
4. \(1.5~\text{m}\)
Subtopic: Wave Motion |
69%
Level 2: 60%+
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The displacement of a traveling wave is given by \(y=C\sin\dfrac{2\pi}{\lambda}({at}-x)\) where \(t\) is time, \(x\) is distance and \(\lambda\) is the wavelength, all in SI units. The frequency of the wave is:
| 1. | \(\dfrac{2\pi\lambda}{a}\) | 2. | \(\dfrac{2\pi a}{\lambda}\) |
| 3. | \(\dfrac{\lambda}{a}\) | 4. | \(\dfrac{a}{\lambda}\) |
Subtopic: Wave Motion |
80%
Level 1: 80%+
NEET - 2024
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The wave described by \(y = 0.25\sin(10\pi x-2\pi t),\) where \(x\) and \(y\) are in metres and \(t\) in seconds, is a wave traveling along the:
| 1. | \(-\text{ve}~x\) direction with frequency \(1\) Hz. |
| 2. | \(+\text{ve}~x\) direction with frequency \(\pi\) Hz and wavelength \(\lambda = 0.2~\text{m}\). |
| 3. | \(+\text{ve}~x\) direction with frequency \(1\) Hz and wavelength \(\lambda = 0.2~\text{m}\). |
| 4. | \(-\text{ve}~x\) direction with amplitude \(0.25\) m and wavelength \(\lambda = 0.2~\text{m}\). |
Subtopic: Wave Motion |
85%
Level 1: 80%+
NEET - 2008
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The displacement of a particle is given by \(y = 5\times 10^{-4}\sin\left(100t-50x\right),\) where \(x\) is in metres and \(t\) is in seconds. The velocity of the wave is:
1. \(5000~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.5~\text{m/s}\)
4. \(300~\text{m/s}\)
1. \(5000~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.5~\text{m/s}\)
4. \(300~\text{m/s}\)
Subtopic: Wave Motion |
90%
Level 1: 80%+
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The equation of a progressive wave is given by \(y = 4\sin\left\{ \pi\left(\frac{t}{5}-\frac{x}{9}\right)+\frac{\pi}{6}\right\}\), where \(x\) and \(y\) are in metres and \(t\) in seconds.
Which of the following is correct?
1. \(v = 5~\text{m/s}\)
2. \(\lambda = 18~\text{m}\)
3. \(A = 0.04~\text{m}\)
4. \(\nu= 50~\text{Hz}\)
Which of the following is correct?
1. \(v = 5~\text{m/s}\)
2. \(\lambda = 18~\text{m}\)
3. \(A = 0.04~\text{m}\)
4. \(\nu= 50~\text{Hz}\)
Subtopic: Wave Motion |
86%
Level 1: 80%+
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The mathematical forms for three sinusoidal traveling waves are given by:
Wave \(1\): \(y(x,t)= (2~\text{cm})\sin(3x-6t)\)
Wave \(2\): \(y(x,t)= (3~\text{cm})\sin(4x-12t)\)
Wave \(3\): \(y(x,t)= (4~\text{cm})\sin(5x-11t)\)
where \(x\) is in meters and \(t\) is in seconds. Of these waves:
Wave \(1\): \(y(x,t)= (2~\text{cm})\sin(3x-6t)\)
Wave \(2\): \(y(x,t)= (3~\text{cm})\sin(4x-12t)\)
Wave \(3\): \(y(x,t)= (4~\text{cm})\sin(5x-11t)\)
where \(x\) is in meters and \(t\) is in seconds. Of these waves:
| 1. | Wave \(1\) has the highest wave speed as well as the maximum transverse string speed. |
| 2. | Wave \(2\) has the highest wave speed, while Wave \(1\) has the maximum transverse string speed. |
| 3. | Wave \(3\) has the highest wave speed as well as the maximum transverse string speed. |
| 4. | Wave \(2\) has the highest wave speed, while Wave \(3\) has the maximum transverse string speed. |
Subtopic: Wave Motion |
74%
Level 2: 60%+
The equation \(y(x,t) = 0.005 \cos (\alpha x- \beta t)\) describes a wave traveling along the \(x\text-\)axis. If the wavelength and the time period of the wave are \(0.08~\text{m}\) and \(2.0~\text{s}\), respectively, then \(\alpha\) and \(\beta\) in appropriate units are:
1. \(\alpha = 25.00\pi, \beta = \pi\)
2. \(\alpha = \frac{0.08}{\pi}, \beta = \frac{2.0}{\pi}\)
3. \(\alpha = \frac{0.04}{\pi}, \beta = \frac{1.0}{\pi}\)
4. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
1. \(\alpha = 25.00\pi, \beta = \pi\)
2. \(\alpha = \frac{0.08}{\pi}, \beta = \frac{2.0}{\pi}\)
3. \(\alpha = \frac{0.04}{\pi}, \beta = \frac{1.0}{\pi}\)
4. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
Subtopic: Wave Motion |
87%
Level 1: 80%+
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