The displacement of a particle is given by $y=5\times {10}^{-4}\mathrm{sin}(100t-50x)$,
where x is in metres and t is in seconds. The velocity of the wave is**:**

1. 5000 *m*/*sec*

2. 2 *m*/*sec*

3. 0.5 *m*/*sec*

4. 300 *m*/*sec*

Subtopic: Wave Motion |

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A tuning fork makes \(256\) vibrations per second in air. When the velocity of sound is \(330\) m/s, then the wavelength of the tone emitted is:

1. \(0.56\) m

2. \(0.89\) m

3. \(1.11\) m

4. \(1.29\) m

1. \(0.56\) m

2. \(0.89\) m

3. \(1.11\) m

4. \(1.29\) m

Subtopic: Wave Motion |

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The equation \(y(x,t) = 0.005 ~cos (\alpha x- \beta t)\) describes a wave traveling along the x-axis. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\mathrm{\alpha}$ and $\mathrm{\beta}$ in appropriate units are:

1. $\mathrm{\alpha}=25.00$ $\mathrm{\pi},$ $\mathrm{\beta}=\mathrm{\pi}$

2. $\mathrm{\alpha}=\frac{0.08}{\mathrm{\pi}},$ $\mathrm{\beta}=\frac{2.0}{\mathrm{\pi}}$

3. $\mathrm{\alpha}=\frac{0.04}{\mathrm{\pi}},$ $\mathrm{\beta}=\frac{1.0}{\mathrm{\pi}}$

4. $\mathrm{\alpha}=12.50$ $\mathrm{\pi},$ $\mathrm{\beta}=\frac{\mathrm{\pi}}{2.0}$

Subtopic: Wave Motion |

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If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:

1. | the pulse is traveling along the negative x axis. |

2. | the speed of the pulse is \(4\) m/s. |

3. | the amplitude of the pulse is \(5\) m. |

4. | all of these. |

Subtopic: Wave Motion |

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The equation of a progressive wave is given by $y=4\mathrm{sin}\left\{\pi \left(\frac{{\displaystyle t}}{{\displaystyle 5}}-\frac{{\displaystyle x}}{{\displaystyle 9}}\right)+\frac{{\displaystyle \pi}}{{\displaystyle 6}}\right\}$.

Which of the following is correct?

1. *v* = 5 *m* / sec

2. *λ* = 18 *m*

3. *a* = 0.04 *m*

4. *n = 50 *Hz

Subtopic: Wave Motion |

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From NCERT

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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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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 wave described by y=0.25 sin(10$\pi x-2\pi t$), where x and y are in metres and t in seconds, is a wave traveling along the:

1. | -ve x direction with frequency 1 Hz |

2. | +ve x direction with frequency π Hz and wavelength λ =0.2 m |

3. | +ve x direction with frequency 1 Hz and wavelength λ = 0.2 m |

4. | - ve x direction with amplitude 0.25 m and wavelength λ = 0.2 m |

Subtopic: Wave Motion |

84%

From NCERT

NEET - 2008

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Given the equation for a wave on the string, y = 0.5 sin(5x - 3t) where y and x are in metres and t in seconds, the ratio of the maximum speed of particle to the speed of wave is:

1. | 1:1 | 2. | 5:2 |

3. | 3:2 | 4. | 4:5 |

Subtopic: Wave Motion |

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Three progressive waves \(A,\) \(B\) and \(C\) are shown below. With respect to wave \(A,\)

1. | wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads by \(\pi/2\). |

2. | wave \(C\) leads in phase by \(\pi\) and wave \(B\) lags behind by \(\pi\). |

3. | wave \(C\) lags behind in phase by \(\pi/2\) and wave \(B\) leads behind by \(\pi\). |

4. | wave \(C\) lags behind in phase by \(\pi\) and wave \(B\) leads by \(\pi\). |

Subtopic: Wave Motion |

80%

From NCERT

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