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%
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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. 
\(4\pi~\text{rad}\)
Subtopic:  Wave Motion |
 66%
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. \(2.07\) radians
2. \(0.5\) radians
3. \(1.5\) radians
4. \(1.07\) radians

Subtopic:  Wave Motion |
 61%
From NCERT
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. \(1.5~\text{m}\)
Subtopic:  Wave Motion |
 68%
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:  Wave Motion |
 84%
From NCERT
NEET - 2008
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The displacement of a particle is given by \(y = 5\times 10^{-4}\sin(100t-50x),\) 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. \(300~\text{m/s}\)
Subtopic:  Wave Motion |
 89%
From NCERT
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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. \(\nu= 50~\text{Hz}\)
Subtopic:  Wave Motion |
 85%
From NCERT
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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:
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 |
 72%
From NCERT
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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. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
Subtopic:  Wave Motion |
 86%
From NCERT
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Given the equation for a wave on the string, \(y = 0.5\sin(5x-3t)\) where \(y\) and \(x\) are in metres and \(t\) in seconds, the ratio of the maximum speed of particle to the speed of wave is:
1. \(1:1\) 2. \(5:2\)
3. \(3:2\) 4. \(4:5\)
Subtopic:  Wave Motion |
 83%
From NCERT
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