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A hospital uses an ultrasonic scanner to locate tumors in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is \(1.7~\text{km/s}\)? The operating frequency of the scanner is \(4.2~\text{MHz}\).

1. \(3.0 \times10^{-4}~\text{m}\)

2. \(4.0 \times10^{-4}~\text{m}\)

3. \(3.5 \times10^{-4}~\text{m}\)

4. \(2.0 \times10^{-4}~\text{m}\)

Subtopic: Speed of Sound |

77%

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A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 sin ( 36t + 0.018x + {\pi \over 4})\) where x and y are in cm and t in sec. The positive direction of x is from left to right. What is the shortest distance between two successive crests in the wave?

1. | 1.3 m | 2. | 3.0 m |

3. | 2.5 m | 4. | 3.5 m |

Subtopic: Wave Motion |

67%

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For the travelling harmonic wave, \(y(x,t) = 2.0\ cos\ 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:

1. \(0.8 \pi\ \text{rad}\)

2.\(\pi\ \text{rad}\)

3. \(6.4\pi\ \text{rad}\)

4. \(4\pi\ \text{rad}\)

Subtopic: Wave Motion |

66%

From NCERT

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The transverse displacement of a string (clamped at both ends) is given by;

\(y(x,t)=0.06\sin\Big(\frac{2\pi}{3}x\Big)\cos(120\pi t)\)

where \(x\) and \(y\) are in metre and \(t\) in second. The length of the string is \(1.5\) m and its mass is \(3\times10^{-2}\) kg. The tension in the string is:

1. \(540\) N

2. \(648\) N

3. \(200\) N

4. \(425\) N

\(y(x,t)=0.06\sin\Big(\frac{2\pi}{3}x\Big)\cos(120\pi t)\)

where \(x\) and \(y\) are in metre and \(t\) in second. The length of the string is \(1.5\) m and its mass is \(3\times10^{-2}\) kg. The tension in the string is:

1. \(540\) N

2. \(648\) N

3. \(200\) N

4. \(425\) N

Subtopic: Speed of Sound |

84%

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\(y = 2\cos(3x)\sin(10t)\) represents:

1. | a stationary wave |

2. | a travelling wave |

3. | both stationary and travelling wave |

4. | none of the above |

Subtopic: Standing Waves |

63%

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A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45 Hz. The mass of the wire is $3.5\times {10}^{-2}$ kg and its linear mass density is$4.0\times {10}^{-2}$ kg/m. What is the speed of the transverse wave on the string?

1. 74.31 m/s

2. 75.70 m/s

3. 78.75 m/s

4. 72 m/s

Subtopic: Travelling Wave on String |

65%

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A one-meter long tube open at one end, with a movable piston at the other end, shows resonance with a fixed frequency source (a tuning fork of frequency 340 Hz) when the minimum tube length is 25.5 cm. The speed of sound in air at the temperature of the experiment is: (The edge effects may be neglected.)

1. 324.16 m/s

2. 320 m/s

3. 345 m/s

4. 346.8 m/s

Subtopic: Standing Waves |

67%

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A steel rod \(100\) cm long is clamped at its middle. The fundamental frequency of the longitudinal vibrations of the rod is given to be \(2.53\) kHz. What is the speed of sound in steel?

1. \(5.06\) km/s

2. \(5.12\) km/s

3. \(4.29\) km/s

4. \(4.01\) km/s

Subtopic: Standing Waves |

73%

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Two sitar strings, A and B, playing the note 'Ga,' are slightly out of tune and produce 6 Hz beats. The tension in the string A is slightly reduced, and the beat frequency is found to be reduced to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

1. 316 Hz

2. 318 Hz

3. 319 Hz

4. 314 Hz

Subtopic: Beats |

87%

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A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/sec. What is the speed of sound for an observer standing on the station’s platform?

1. 332 m/s

2. 360 m/s

3. 344 m/s

4. 350 m/s

Subtopic: Speed of Sound |

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