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Q. No.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: Â Wave Motion |
 87%
From NCERT
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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: Â Wave Motion |
 65%
From NCERT
AIPMT - 2004
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Two progressive waves are represented by, \(y_1=5\sin(200t-3.14x)\) and
\(y_2=10\sin\left(200t-3.14x+\frac{\pi}{3}\right)\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. \(\frac{100}{\pi}~\text{m}\)
2. \(\frac{1}{3}~\text{m}\)
3. \(3.14\times \frac{\pi}{3}~\text{m}\)
4. \(\frac{\pi^2}{9}~\text{m}\)
\(y_2=10\sin\left(200t-3.14x+\frac{\pi}{3}\right)\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. \(\frac{100}{\pi}~\text{m}\)
2. \(\frac{1}{3}~\text{m}\)
3. \(3.14\times \frac{\pi}{3}~\text{m}\)
4. \(\frac{\pi^2}{9}~\text{m}\)
Subtopic: Â Wave Motion |
 75%
From NCERT
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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: Â Wave Motion |
 85%
From NCERT
NEET - 2008
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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: Â Wave Motion |
 85%
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In the wave equation, \({y}=0.5 \sin \dfrac{2 \pi}{\lambda}(400 {t}-{x}) ~{\text m}, \) the velocity of the wave will be:
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
1. \(200~\text{m/s}\)
2. \(200 \sqrt 2~\text{m/s}\)
3. \(400~\text{m/s}\)
4. \(400 \sqrt 2~\text{m/s}\)
Subtopic: Â Wave Motion |
 92%
From NCERT
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A longitudinal wave is represented by \(x = 10 ~\sin ~2 \pi \left( nt- {\dfrac x \lambda}\right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to:
1. \(2 \pi\) cm
2. \(5 \pi\) cm
3. \(\pi\) cm
4. \({\dfrac {5 \pi} 2}\) cm
1. \(2 \pi\) cm
2. \(5 \pi\) cm
3. \(\pi\) cm
4. \({\dfrac {5 \pi} 2}\) cm
Subtopic: Â Wave Motion |
 88%
From NCERT
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A transverse wave travels along the Z-axis. The particles of the medium must move:
| 1. | along the Z-axis | 2. | along the X-axis |
| 3. | along the Y-axis | 4. | in the X-Y plane |
Subtopic: Â Wave Motion |
 83%
From NCERT
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Two sine waves travel in the same direction in a medium. The amplitude of each wave is \(A\) and the phase difference between the two waves is \(120^\circ.\) The resultant amplitude will be:
1. \(A\)
2. \(2A\)
3. \(4A\)
4. \(\sqrt2 A\)
Subtopic: Â Wave Motion |
 86%
From NCERT
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