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For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?

1. \(\pi y_0\)

2. \(2\pi y_0\)

3. \(\pi y_0/2\)

4. \(4\pi y_0\)

Subtopic: Wave Motion |

73%

From NCERT

AIPMT - 1998

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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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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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Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:

1. $\frac{2u}{\lambda}$

2. $\frac{u}{\lambda}$

3. $\sqrt{\mu \lambda}$

4. $\frac{\mu}{2\lambda}$

Subtopic: Beats |

58%

From NCERT

AIPMT - 2000

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A string is cut into three parts, having fundamental frequencies n_{1}, n_{2}, and n_{3 }respectively.
The original fundamental frequency "n" is related by the expression:

1. $\frac{1}{n}=\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}+\frac{1}{{n}_{3}}$

2. $n={n}_{1}\times {n}_{2}\times {n}_{3}$

3. $n={n}_{1}+{n}_{2}+{n}_{3}$

4. $n=\frac{{n}_{1}+{n}_{2}+{n}_{3}}{3}$

Subtopic: Standing Waves |

84%

From NCERT

AIPMT - 2000

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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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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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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 |

75%

From NCERT

AIPMT - 2001

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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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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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