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The mathematical forms for three sinusoidal traveling waves are given by:

Wave 1 : y(x,t) = (2cm) sin(3x–6t)

Wave 2 : y(x,t) = (3cm) sin(4x–12t)

Wave 3 : y(x,t) = (4cm) sin(5x–11t)

where x is in meters and t is in seconds. Of these waves :

1. | Wave 1 has the highest wave speed as well as the maximum transverse string speed. |

2. | Wave 2 has the highest wave speed, while Wave 1 has the maximum transverse string speed. |

3. | Wave 3 has the highest wave speed as well as the maximum transverse string speed. |

4. | Wave 2 has the highest wave speed, while Wave 3 has the maximum transverse string speed. |

Subtopic: Wave Motion |

71%

From NCERT

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A string of length 3 m and a linear mass density of 0.0025 kg/m is fixed at both ends. One of its resonance frequencies is 252 Hz. The next higher resonance frequency is 336 Hz. Then the fundamental frequency will be:

1. 84 Hz

2. 63 Hz

3. 126 Hz

4. 168 Hz

Subtopic: Standing Waves |

76%

From NCERT

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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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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 source of unknown frequency gives \(4\) beats/s when sounded with a source of known frequency of \(250~\text{Hz}\). The second harmonic of the source of unknown frequency gives five beats per second when sounded with a source of frequency of \(513~\text{Hz}\). The unknown frequency will be:

1. | \(246~\text{Hz}\) | 2. | \(240~\text{Hz}\) |

3. | \(260~\text{Hz}\) | 4. | \(254~\text{Hz}\) |

Subtopic: Beats |

77%

From NCERT

AIPMT - 2013

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The fundamental frequency of a closed organ pipe of a length \(20\) cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

1. | \(80\) cm | 2. | \(100\) cm |

3. | \(120\) cm | 4. | \(140\) cm |

Subtopic: Standing Waves |

77%

From NCERT

NEET - 2015

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A uniform rope, of length \(L\) and mass \(m_1\), hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\)${\mathrm{}}_{}$. The ratio \(\frac{\lambda_2}{\lambda_1}\) is:

1. \(\sqrt{\frac{m_1+m_2}{m_2}}\)

2. \(\sqrt{\frac{m_2}{m_1}}\)

3. \(\sqrt{\frac{m_1+m_2}{m_1}}\)

4. \(\sqrt{\frac{m_1}{m_2}}\)

Subtopic: Travelling Wave on String |

69%

From NCERT

NEET - 2016

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An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is \(50\) cm. The next larger length of the column resonating with the same tuning fork will be:

1. | \(100\) cm | 2. | \(150\) cm |

3. | \(200\) cm | 4. | \(66.7\) cm |

Subtopic: Standing Waves |

79%

From NCERT

NEET - 2016

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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 |

86%

From NCERT

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The speed of sound in a medium is \(v\). If the density of the medium is doubled at constant pressure, what will be the new speed of sound?

1. | \(\sqrt{2} v \) | 2. | \(v \) |

3. | \(\frac{v}{\sqrt{2}} \) | 4. | \(2v\) |

Subtopic: Speed of Sound |

78%

From NCERT

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