A $100$ cm wire of mass $40$ g is fixed at both ends. A tuning fork, vibrating at a frequency of $50$ Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is:

1. $400$ N 2. $100$ N

3. $25$ N 4. $1600$ N

Subtopic: Standing Waves |

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Q6:

If the absolute temperature increases by

1 %

$1\%$ , the frequency of an organ pipe will:

1.	increase by $1\%$	2.	decrease by $1\%$
3.	increase by $0.5\%$	4.	decrease by $0.5\%$

Subtopic: Speed of Sound |

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Q7:

A heavy uniform rope

P Q

$PQ$ is suspended from the ceiling. The lowest end of the rope is given a sharp transverse "shake" (or vibration) so as to cause a pulse. This pulse travels upward. As it travels upward, its speed:

1.	increases	2.	decreases
3.	first increases and then decreases	4.	remains constant

Subtopic: Travelling Wave on String |

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Q8:

When two identical loudspeakers playing the same frequency are placed equidistant from an observer, a sound of

60

$60$ dB is heard if the sources are in phase with each other. However, if the two speakers are out of phase, no sound is heard. If the speakers are played with a phase difference of

90^{\circ},

$90^\circ,$ the sound heard will be:
1.

30 \sqrt{2}

$30\sqrt2$ dB
2.

(60 + \sqrt{2})

$(60+\sqrt2)$ dB
3.

57

$57$ dB
4.

60 \sqrt{2}

$60\sqrt2$ dB

Subtopic: Pressure Wave in Sound |

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Q9:

The equation of vibration of a taut string, fixed at both ends, is given by;

y = (3 mm) cos (\frac{π x}{10 cm}) sin (800 π s^{- 1} t) .

$y=(3~\text{mm})~\text{cos}\left(\dfrac{\pi x}{10~\text{cm}}\right)~\text{sin}(800\pi~\text{s}^{-1}{t}).$ The positions of the nodes are:

1.	$x= 0~\text{cm}, 10~\text{cm}, 20~\text{cm},....$
2.	$x= 0~\text{cm}, 20~\text{cm}, 40~\text{cm},....$
3.	$x= 5~\text{cm}, 10~\text{cm}, 15~\text{cm},....$
4.	$x= 5~\text{cm}, 15~\text{cm}, 25~\text{cm},....$

Subtopic: Beats |

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Q10:

Sinusoidal sound waves of the same frequency travelling in air along the

x

$x$ -axis and the

y

$y$ -axis arrive in phase with each other at the origin. Their amplitudes are equal to

A

$A$ (each). The amplitude of the vibration at the origin is:

1.

A

$A$
2.

\sqrt{2} A

$\sqrt 2A$
3.

2 A

$2A$
4.

(2 + \sqrt{2}) A

$(2+\sqrt2)A$

Subtopic: Wave Motion |

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Q11:

The fundamental frequencies of a closed pipe and an open pipe are identical. The first overtone for the closed pipe is

f_{c}

$f_c$ and for the open pipe is

f_{o} .

$f_o.$ Their ratio

\frac{f_{c}}{f_{o}}

$\dfrac{f_c}{f_o}$ is:

1.	$1$	2.	$1/2$
3.	$2/3$	4.	$3/2$

Subtopic: Standing Waves |

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Q12:

The square of the speed of sound in a mono-atomic gas is proportional to:

1.	its internal energy
2.	its internal energy per unit volume
3.	its internal energy per unit mass
4.	its internal energy per unit temperature

Subtopic: Speed of Sound |

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Q13:

A string fixed at both ends is under tension

T .

$T.$ It has a length

L,

$L,$ and mass

m .

$m.$ The fundamental frequency of the vibration is:
1.

\frac{1}{2 L} \sqrt{\frac{T}{m}}

$\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}$
2.

\frac{1}{4 L} \sqrt{\frac{T}{m}}

$\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}$
3.

\frac{1}{2} \sqrt{\frac{T L}{2 m}}

$\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}$
4.

\frac{1}{2} \sqrt{\frac{T}{m L}}

$\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}$

Subtopic: Travelling Wave on String |

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Q14:

The first overtone of a closed pipe has a frequency

f_{c} .

$f_c.$ A frequency that is

2 f_{c}

$2f_c$ can be excited from an open pipe of the same length but vibrating in its:

1.	$2^{\text{nd}}$ harmonic	2.	$3^{\text{rd}}$ harmonic
3.	$6^{\text{th}}$ harmonic	4.	$12^{\text{th}}$ harmonic

Subtopic: Standing Waves |

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A $100$ cm wire of mass $40$ g is fixed at both ends. A tuning fork, vibrating at a frequency of $50$ Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is:

1. $400$ N 2. $100$ N

3. $25$ N 4. $1600$ N

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A 100100 cm wire of mass 4040 g is fixed at both ends. A tuning fork, vibrating at a frequency of 5050 Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is: 1. 400400 N 2. 100100 N 3. 2525 N 4. 16001600 N

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A $100$ cm wire of mass $40$ g is fixed at both ends. A tuning fork, vibrating at a frequency of $50$ Hz, sets the wire into resonance in its fundamental mode. Then, the tension in the wire is:

1. $400$ N 2. $100$ N

3. $25$ N 4. $1600$ N