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Q. No.

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. \(300~\text{m/s}\)
Q1:
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Subtopic:  Wave Motion |
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A tuning fork makes \(256\) vibrations per second in air. When the velocity of sound is \(330\) m/s, then the wavelength of the tone emitted is:
1. \(0.56\) m
2. \(0.89\) m
3. \(1.11\) m
4. \(1.29\) m
Q2:
 86% From NCERT 
Subtopic:  Wave Motion |
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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. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
Q3:
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Subtopic:  Wave Motion |
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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.
Q4:
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Subtopic:  Wave Motion |
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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. \(\nu= 50~\text{Hz}\)
Q5:
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Subtopic:  Wave Motion |
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A wave traveling in the +ve \(x\text-\)direction having maximum displacement along \(y\text-\)direction as \(1~\text{m}\), wavelength \(2\pi~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
1. \(y=\sin (2 \pi x-2 \pi t)\)
2. \(y=\sin (10 \pi x-20 \pi t)\)
3. \(y=\sin (2 \pi x+2 \pi t)\)
4. \( y=\sin (x-2 t)\)

Q6:
 86% From NCERT AIPMT - 2013
Subtopic:  Wave Motion |
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If a wave is travelling in a positive \(x\text-\)direction with \(A= 0.2~\text{m}\), \(v=360~\text{m/s}\), and \(\lambda= 60~\text{m}\), then the correct expression for the wave will be:
1.  \({y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]\)
2. \({y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]\)
3. \({y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]\)
4. \(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\)
Q7:
 86% From NCERT AIPMT - 2002
Subtopic:  Wave Motion |
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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 \(\lambda = 0.2~\text{m}\).
Q8:
 84% From NCERT NEET - 2008
Subtopic:  Wave Motion |
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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. \(4:5\)
Q9:
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Subtopic:  Wave Motion |
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Three progressive waves \(A,\) \(B\) and \(C\) are shown below. With respect to wave \(A\text{:}\)
              
1. Wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads by \(\pi/2\).
2. Wave \(C\) leads in phase by \(\pi\) and wave \(B\) lags behind by \(\pi\).
3. Wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads by \(\pi\).
4. Wave \(C\) lags behind in phase by \(\pi\) and wave \(B\) leads by \(\pi\).
Q10:
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Subtopic:  Wave Motion |
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