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If the equation of a wave is represented by:

$y$ $=$ ${10}^{-4}$ $\mathrm{sin}(100t$ $-$ $\frac{x}{10})m$, then the velocity of wave will be:

1. 100 m/s

2. 4 m/s

3. 1000 m/s

4. 0.00 m/s

Subtopic: Wave Motion |

89%

From NCERT

AIPMT - 2001

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Two waves have the following equations:

${x}_{1}$ $=$ $a$ $\mathrm{sin}$ $(\omega t$ $+$ ${\varphi}_{1})$

${x}_{2}$ $=$ $a$ $\mathrm{sin}$ $(\omega t$ $+$ ${\varphi}_{2})$

If in the resultant wave, the frequency and amplitude remain equal to the amplitude of superimposing waves, then the phase difference between them will be:

1. $\frac{\mathrm{\pi}}{6}$

2. $\frac{2\mathrm{\pi}}{3}$

3. $\frac{\mathrm{\pi}}{4}$

4. $\frac{\mathrm{\pi}}{3}$

Subtopic: Standing Waves |

74%

From NCERT

AIPMT - 2001

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If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become:

1. $\frac{n}{4}$

2. $\sqrt{2}$ $n$ $$

3. n

4. $\frac{n}{\sqrt{2}}$

Subtopic: Standing Waves |

65%

From NCERT

AIPMT - 2001

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If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:

1. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |

2. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |

3. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |

4. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |

Subtopic: Wave Motion |

85%

From NCERT

AIPMT - 2002

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The phase difference between two waves, represented by

$\begin{array}{l}{\mathrm{y}}_{1}={10}^{-6}\mathrm{sin}\{100\mathrm{t}+(\mathrm{x}/50)+0.5\}\mathrm{m}\\ {\mathrm{y}}_{2}={10}^{-6}\mathrm{cos}\{100\mathrm{t}+\left(\frac{\mathrm{x}}{50}\right)\}\mathrm{m}\end{array}$

where X is expressed in metres and t is expressed in seconds, is approximate:

1. 2.07 radians

2. 0.5 radians

3. 1.5 radians

4. 1.07 radians

Subtopic: Wave Motion |

59%

From NCERT

AIPMT - 2004

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A cylindrical tube (L = 125 cm) is resonant with a tuning fork at a frequency of 330 Hz. If it is filled with water, then to get the resonance again, the minimum length of the water column will be: $({v}_{air}$ $=$ $330$ $m/s)$

1. | 50 cm | 2. | 60 cm |

3. | 25 cm | 4. | 20 cm |

Subtopic: Standing Waves |

From NCERT

AIPMT - 1999

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A point source emits sound equally in all directions in a non-absorbing medium.
Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:

1. \(3:2\)

2. \(2:3\)

3. \(9:4\)

4. \(4:9\)

Subtopic: Energy of Waves |

73%

From NCERT

AIPMT - 2005

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If a standing wave having 3 nodes and 2 antinodes is formed within 1.21 Å distance, then the wavelength of the standing wave will be:

1. 1.21 Å

2. 2.42 Å

3. 0.605 Å

4. 4.84 Å

Subtopic: Standing Waves |

78%

From NCERT

AIPMT - 1998

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Two vibrating tuning forks produce progressive waves given by \(Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}\) and \(Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}\). The number of beats produced per minute is:

1. | \(3\) | 2. | \(360\) |

3. | \(180\) | 4. | \(60\) |

Subtopic: Beats |

57%

From NCERT

AIPMT - 2005

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The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + $\alpha $), where δ = $\alpha $ + $\pi $/2, then the resultant wave can be represented by:

1. a circle (c.w)

2. a circle (a.c.w)

3. an ellipse (c.w)

4. an ellipse (a.c.w)

Subtopic: Standing Waves |

52%

From NCERT

AIPMT - 2000

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