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 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 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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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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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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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.
Subtopic:  Types of Waves |
 81%
From NCERT
AIPMT - 2006
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The speed of sound in nitrogen gas compared to that in helium gas at 300 K is:

1. 27

2. 17

3. 35

4. 65

Subtopic:  Speed of Sound |
From NCERT
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A triangular transverse wave is propagating in the positive X-direction. The velocity of P at this instant will be:

1. vertically upward.
2. vertically downward.
3. at rest.
4. cannot be determined.

Subtopic:  Wave Motion |
 67%
From NCERT
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