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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Two sources of sound placed close to each other, are emitting progressive waves given by,
\(y_1=4\sin 600\pi t\) and \(y_2=5\sin 608\pi t\).
An observer located near these two sources of sound will hear:

1. \(4\) beats per second with intensity ratio \(25:16\) between waxing and waning
2. \(8\) beats per second with intensity ratio \(25:16\) between waxing and waning
3. \(8\) beats per second with intensity ratio \(81:1\) between waxing and waning
4. \(4\) beats per second with intensity ratio \(81:1\) between waxing and waning

Subtopic:  Beats |
 60%
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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Sound waves travel at \(350\) m/s through warm air and at \(3500\) m/s through brass. The wavelength of a \(700\) Hz acoustic wave as it enters brass from warm air:
 

1. increase by a factor of \(20\) 
2. increase by a factor of \(10\)
3. decrease by a factor of \(20\)
4. decrease by a factor of \(10\) 
Subtopic:  Speed of Sound |
 77%
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 tuning fork of frequency \(512\) Hz makes \(4\) beats/s with the vibrating string of a piano. The beat frequency decreases to \(2\) beats/s when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:
1. \(510\) Hz
2. \(514\) Hz
3. \(516\) Hz
4. \(508\) Hz

Subtopic:  Beats |
 70%
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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Each of the two strings of lengths 51.6 cm and 49.1 cm is tensioned separately by 20 N of force. The mass per unit length of both strings is the same and equals 1 g/m. When both the strings vibrate simultaneously, the number of beats is:

1. 5 2. 7
3. 8 4. 3
Subtopic:  Beats |
 56%
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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Two sound waves with wavelengths 5.0 m and 5.5 m, respectively, propagate in gas with a velocity of 330 m/s. How many beats per second can we expect?

1. 12

2. 0

3. 1

4. 6

Subtopic:  Beats |
 75%
From NCERT
AIPMT - 2006
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