A wave traveling in the +ve \(x\)-direction having maximum displacement along \(y\)-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. \( y=\sin (x-2 t)\)

Subtopic:  Wave Motion |
 86%
From NCERT
AIPMT - 2013
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The equation of a simple harmonic wave is given by \(y=3\sin \frac{\pi}{2}(50t-x)\) where \(x \) and \(y\) are in meters and \(t\) is in seconds. The ratio of maximum particle velocity to the wave velocity is:
1. \(\frac{3\pi}{2}\)
2. \(3\pi\)
3. \(\frac{2\pi}{3}\)
4. \(2\pi\)

Subtopic:  Wave Motion |
 74%
From NCERT
AIPMT - 2012
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Two waves are represented by the equations y1=a sin(ωt+kx+0.57) m and
 y2=acos(ωt+kx) m, where \(x\) is in metres and \(t\) in seconds. The phase difference between them is:
1. \(1.25\) rad
2. \(1.57\) rad
3. \(0.57\) rad
4. \(1.0\) rad

Subtopic:  Wave Motion |
 67%
From NCERT
AIPMT - 2011
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A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. πA/2

2. πA

3. 2πA

4. A

Subtopic:  Wave Motion |
 84%
From NCERT
AIPMT - 2010
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A wave in a string has an amplitude of 2 cm. The wave travels in the positive direction of the x-axis with a speed of 128 m/s and it is noted that 5 complete waves fit in the 4 m length of the string. The equation describing the wave is:

1. y = (0.02)m sin(7.85x+1005t)
2. y = (0.02)m sin(15.7x -2010t)
3. y = (0.02)m sin(15.7x+2010t)
4. y = (0.02)m sin(7.85x -1005t) 

Subtopic:  Wave Motion |
 72%
From NCERT
AIPMT - 2009
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The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:

1. –ve x-direction with frequency \(1\) Hz
2. +ve x-direction with frequency \(\pi\) Hz and wavelength  \(\lambda=0.2\) m
3. +ve x-direction with frequency \(1\) Hz and wavelength  \(\lambda=0.2\) m
4. –ve x-direction with amplitude \(0.25\) m and wavelength  \(\lambda=0.2\) m

Subtopic:  Wave Motion |
 84%
From NCERT
AIPMT - 2008
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A transverse wave propagating along the x-axis is represented by:
\(y=(x,t)=8.0\mathrm{sin}(0.5\pi x-4\pi t-\frac{\pi}{4})\) where \(x\) is in meters and \(t\) in seconds. The speed of the wave is: 
1. \(4\pi\) m/s
2. \(0.5\) m/s
3. \(\frac{\pi}{4}\) m/s
4. \(8\) m/s

Subtopic:  Wave Motion |
 82%
From NCERT
AIPMT - 2006
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