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Q. No.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 58%
Level 3: 35%-60%
Hints
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
1. \(30\sqrt2 \) dB
2. \((60+\sqrt2) \) dB
3. \(57\) dB
4. \(60\sqrt2 \) dB
Subtopic: Ā Pressure Wave in Sound |
Level 4: Below 35%
Hints
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 |
Level 4: Below 35%
Hints
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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 |
Level 4: Below 35%
Hints
The fundamental frequencies of a closed pipe and an open pipe are identical. The first overtone for the closed pipe is \(f_c\) and for the open pipe is \(f_o.\) Their ratio \(\dfrac{f_c}{f_o}\) is:
| 1. | \(1\) | 2. | \(1/2\) |
| 3. | \(2/3\) | 4. | \(3/2\) |
Subtopic: Ā Standing Waves |
Ā 70%
Level 2: 60%+
Hints
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: Ā Speed of Sound |
Ā 60%
Level 2: 60%+
Hints
A string fixed at both ends is under tension \(T.\) It has a length \(L,\) and mass \(m.\) The fundamental frequency of the vibration is:
| 1. | \(\dfrac{ 1}{2L} \sqrt {\dfrac{T}{m}}\) | 2. | \(\dfrac{1}{4 L} \sqrt{\dfrac{T}{m}}\) |
| 3. | \(\dfrac{1}{2} \sqrt{\dfrac{TL}{2m}}\) | 4. | \(\dfrac{1}{2} \sqrt{\dfrac{T}{m L}}\) |
Subtopic: Ā Travelling Wave on String |
Ā 58%
Level 3: 35%-60%
Hints
The first overtone of a closed pipe has a frequency \(f_c.\) A frequency that is \(2f_c\) 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: Ā Standing Waves |
Ā 68%
Level 2: 60%+
Hints
The equation of vibration of a taut string, fixed at both ends, is given by: \(y=(4~\text{mm})~\cos\left(\dfrac{\pi x}{30~\text{cm}}\right)~\sin\Big(400\pi s^{-1}t\Big) \)
At which points is the amplitude equal to \(2\) mm?
At which points is the amplitude equal to \(2\) mm?
| 1. | \(x = \) \(10\) cm, \(20\) cm, \(30\) cm, \(40\) cm |
| 2. | \(x=\) \(10\) cm, \(15\) cm, \(30\) cm, \(45\) cm |
| 3. | \(x =\) \(10\) cm, \(20\) cm, \(40\) cm, \(80\) cm |
| 4. | \(x = \) \(10\) cm, \(20\) cm, \(40\) cm, \(50\) cm |
Subtopic: Ā Standing Waves |
Level 3: 35%-60%
Hints
A waveform given by: \(y=3A\sin(\omega t-kx)\)
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
is superposed with another waveform \(y=4A\cos(\omega t-kx).\) The amplitude of the resulting waveform will be:
| 1. | \(7A\) | 2. | \(A\) |
| 3. | \(3.5A\) | 4. | \(5A\) |
Subtopic: Ā Wave Motion |
Ā 85%
Level 1: 80%+
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