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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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A cylindrical tube open at both ends has a fundamental frequency *f _{0}* in the air. The tube is dipped vertically in water such that half its length is inside water. The fundamental frequency of the air column now will be:

1. $\frac{3{f}_{\mathit{0}}}{4}$

2. ${f}_{0}$

3. $\frac{{f}_{\mathit{0}}}{2}$

4. 2${f}_{0}$

Subtopic: Standing Waves |

68%

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The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\mathrm{sin}$ $0.5\mathrm{\pi t}$ $\mathrm{cos}(0.2\mathrm{\pi x}),$ $$ where t is in seconds and x in centimetres. Which of the following is correct?

1. | Wavelength of the component waves is 10 cm. |

2. | The separation between a node and the nearest antinode is 2.5 cm. |

3. | Frequency of the component wave is 0.25 Hz. |

4. | All of these |

Subtopic: Standing Waves |

89%

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Two sound waves given by the equations \(y=A\sin 122 \pi t\) and \(y=A\sin 128 \pi t\) pass through a point simultaneously. The number of beats per second is:

1. | \(6\) | 2. | \(5\) |

3. | \(4\) | 4. | \(3\) |

Subtopic: Beats |

82%

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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 |

83%

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A string of length l is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:

1. 1:2:3: ......

2. 1:3:5:7: ......

3. 1:2:4:8: ..........

4. 1:3:9: ........

Subtopic: Standing Waves |

82%

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Two progressive waves are represented by, \(y_1=5sin(200t-3.14x)\) and

\(y_2=10sin(200t-3.14x+\frac{\pi}{3})\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:

1. $\frac{100}{\mathrm{\pi}}m$

2. $\frac{1}{3}m$

3. $3.14\times \frac{\mathrm{\pi}}{3}\mathrm{m}$

4. $\frac{{\mathrm{\pi}}^{2}}{9}m$

Subtopic: Wave Motion |

72%

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Two waves represented by the following equations are travelling in the same medium \(y_1 = 5 sin2\pi (75t-0.25x)\), \(y_2 = 10 sin2\pi (150t-0.50x)\)${\mathrm{}}_{}$

The intensity ratio \(\frac{I_1}{I_2}\) of the two waves will be:

1. \(1:2\)

2. \(1:4\)

3. \(1:8\)

4. \(1:16\)

Subtopic: Energy of Waves |

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A tuning fork with a frequency of \(800\) Hz produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of \(9.75\) cm, \(31.25\) cm, and \(52.75\) cm. The speed of the sound in the air is:

1. | \(500\) m/s | 2. | \(156\) m/s |

3. | \(344\) m/s | 4. | \(172\) m/s |

Subtopic: Speed of Sound |

74%

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A transverse wave moves from a medium \(A\) to a medium \(B\). In medium \(A\), the velocity of the transverse wave is \(500~\text{ms}^{-1}\) and the wavelength is \(5~\text{m}\). The frequency and the wavelength of the wave in medium \(B\) when its velocity is \(600~\text{ms}^{-1}\), respectively are:

1. | \(120~\text{Hz}\) and \(5~\text{m}\) | 2. | \(100~\text{Hz}\) and \(5~\text{m}\) |

3. | \(120~\text{Hz}\) and \(5~\text{m}\) | 4. | \(100~\text{Hz}\) and \(6~\text{m}\) |

Subtopic: Speed of Sound |

80%

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