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Q. No.

Which one of the following statements is true?

1. Both light and sound waves in the air are transverse.
2. The sound waves in the air are longitudinal while the light waves are transverse.
3. Both light and sound waves in the air are longitudinal.
4. Both light and sound waves can travel in a vacuum.
Q1:
 81% From NCERT AIPMT - 2006
Subtopic:  Types of Waves |
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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. \(300~\text{m/s}\)
Q2:
 89% From NCERT 
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. \(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\)
Q3:
 86% From NCERT AIPMT - 2002
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. \(\alpha = 12.50\pi, \beta = \frac{\pi}{2.0}\)
Q4:
 87% From NCERT 
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.
Q5:
 85% From NCERT 
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. \(4:5\)
Q6:
 83% From NCERT 
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 \(\lambda = 0.2~\text{m}\).
Q7:
 85% From NCERT NEET - 2008
Subtopic:  Wave Motion |
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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. \(\frac{\pi^2}{9}~\text{m}\)
Q8:
 73% From NCERT 
Subtopic:  Wave Motion |
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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. \(1.07~\text{radians}\)

Q9:
 61% From NCERT AIPMT - 2004
Subtopic:  Wave Motion |
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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.
Q10:
 72% From NCERT 
Subtopic:  Wave Motion |
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Next Hint
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