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A rope of uniform mass per unit length \(\mu\) is suspended from the ceiling, hanging under its own weight. If a small transverse pulse is formed at its lower end \(A\), it travels upward with a local speed \(v=\sqrt {\dfrac{\text{tension}}{\text{mass/length}}}\).
                         
The speed of the pulse is:
1. maximum at \(A\), minimum at \(O\)
2. minimum at \(A\), maximum at \(O\)
3. uniform
4. minimum at \(A\) and \(O\), maximum in the middle
Subtopic: Ā Travelling Wave on String |
Ā 72%
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The intensity \((I)\) of a sound wave depends on the distance \((x)\) from the source as:

1. \(I\propto x\) 2. \(I\propto \dfrac1x\)
3. \(I\propto \dfrac1{x^2}\) 4. none of the above
Subtopic: Ā Energy of Waves |
Ā 74%
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If the absolute temperature of a gas is increased by \(1\text{%},\) the speed of sound in the gas:
1. increases by \(\sqrt{1} \text{%}\)
2. decreases by \(\sqrt{1} \text{%}\)
3. increases by \(1\text{%}\)
4. increases by \(0.5\text{%}\)

Subtopic: Ā Speed of Sound |
Ā 66%
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The first overtone of a closed organ pipe of length \(l_1\) matches the fundamental frequency of an open pipe of length \(l_2\). Then,
1. \(l_1 = 2l_2\)
2. \(l_2 = 2l_1\)
3. \(2l_1 = 3l_2\)
4. \(2l_2 = 3l_1\)
Subtopic: Ā Standing Waves |
Ā 67%
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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. \(400\) 2. \(100\)
3. \(25\) 4. \(1600\) N
Subtopic: Ā Standing Waves |
Ā 74%
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If the absolute temperature increases by \(1\%\), 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: Ā Speed of Sound |
Ā 74%
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A heavy uniform rope \(PQ\) 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: Ā Travelling Wave on String |
Ā 57%
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When two identical loudspeakers playing the same frequency are placed equidistant from an observer, a sound of \(60\) 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 \(90^\circ,\) the sound heard will be:
1. \(30\sqrt2\) dB
2. \((60+\sqrt2)\) dB
3. \(57\) dB
4. \(60\sqrt2\) dB
Subtopic: Ā Pressure Wave in Sound |
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The equation of vibration of a taut string, fixed at both ends, is given by; \(y=(3~\text{mm})~\text{cos}\left(\dfrac{\pi x}{10~\text{cm}}\right)~\text{sin}(800\pi~\text{s}^{-1}{t}).\) 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: Ā Beats |
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Sinusoidal sound waves of the same frequency travelling in air along the \(x\)-axis and the \(y\)-axis arrive in phase with each other at the origin. Their amplitudes are equal to \(A\) (each). The amplitude of the vibration at the origin is:
               
1. \(A\)
2. \(\sqrt 2A\)
3. \(2A\)
4. \((2+\sqrt2)A\)
Subtopic: Ā Wave Motion |
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