Q. No.A transverse harmonic wave on a string is described by \(y(x,~t)=3.0 ~\sin(36t+0.018x+\pi/4),\) where \(x\) and \(y\) are in cm and \(t\) is in \(\text s.\) The positive direction of \(x\) is from left to right.
Choose the correct option:
| (a) | The wave is travelling from right to left. |
| (b) | The speed of the wave is \(20~\text{m/s}.\) |
| (c) | The frequency of the wave is \(5.7~\text{Hz}.\) |
| (d) | The least distance between two successive crests in the wave is \(5.7~\text{cm}.\) |
Choose the correct option:
| 1. | (a), (c) | 2. | (a), (b), (c) |
| 3. | (b), (d) | 4. | (d) only |
Subtopic: Standing Waves |
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Two waves executing simple harmonic motion travelling in the same direction with the same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt 3 \) times of amplitude of individual motions. The phase difference between the two motions is:
| 1. | \(30^{\circ}\) | 2. | \(45^{\circ}\) |
| 3. | \(60^{\circ}\) | 4. | \(90^{\circ}\) |
Subtopic: Standing Waves |
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Level 1: 80%+
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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 |
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Given below are two statements:
In the light of the above statements, choose the correct answer from the options given below:
| Assertion (A): | A glass tube partially filled with water represents an open organ pipe. |
| Reason (R): | The open end corresponds to an antinode and the end in contact with water, to a node. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True and (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Standing Waves |
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NEET - 2024
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The displacement of a string is given by \(y (x,t) = 0.06 ~\sin (2πx/3) ~\cos (120πt)\) where \(x\) and \(y\) are in m and \(t\) in s. The length of the string is \(1.5\) m and its mass is \(3.0\times 10^{-2}~\text{kg}\).
Choose the correct option:
| 1. | It represents a progressive wave of frequency \(60\) Hz. |
| 2. | It represents a stationary wave of frequency \(60\) Hz. |
| 3. | It is the result of superposition of two waves of wavelength \(3\) m, frequency \(60\) Hz each travelling with a speed of \(180\) m/s in opposite direction. |
| 4. | Amplitude of this wave is constant. |
Choose the correct option:
| 1. | (a), (c) | 2. | (a), (b), (c) |
| 3. | (b), (c) | 4. | (d) only |
Subtopic: Standing Waves |
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Which of the following statements are true for a stationary wave?
Choose the correct option:
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
| (a) | Every particle has a fixed amplitude which is different from the amplitude of its nearest particle. |
| (b) | All the particles cross their mean position at the same time. |
| (c) | All the particles are oscillating with same amplitude. |
| (d) | There is no net transfer of energy across any plane. |
| (e) | There are some particles which are always at rest. |
1. (a), (c)
2. (a), (b), (d), (e)
3. (b), (d)
4. (c), (d)
Subtopic: Standing Waves |
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The equation of stationary wave along a stretched string is given by; \(y=5 \sin \left ( \dfrac{\pi x}{3} \right ) \cos (40 \pi t)\), where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) in seconds. The separation between two adjacent nodes is:
| 1. | \(1.5~\text{cm}\) | 2. | \(3~\text{cm}\) |
| 3. | \(6~\text{cm}\) | 4. | \(4~\text{cm}\) |
Subtopic: Standing Waves |
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A string is fixed at both ends and set to vibrate in five loops. If the wavelength is \(8\) cm then the length of the string is:
1. \(10 \) cm
2. \(15\) cm
3. \(20\) cm
4. \(25\) cm
Subtopic: Standing Waves |
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A wire of length \(30\) cm, stretched between rigid supports, has its \(\mathrm{n}\)th and \(\mathrm{(n+1)}\)th harmonics at \(400\) Hz and \(450\) Hz, respectively. If the tension in the string is \(2700\) N, its linear mass density is:
| 1. | \(3\) kg/m | 2. | \(6\) kg/m |
| 3. | \(9\) kg/m | 4. | \(1\) kg/m |
Subtopic: Standing Waves |
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The length of the string of a musical instrument is \(90\) cm and has a fundamental frequency of \(120\) Hz. Where should it be pressed to produce a fundamental frequency of \(180\) Hz?
| 1. | \(75\) cm | 2. | \(60\) cm |
| 3. | \(45\) cm | 4. | \(80\) cm |
Subtopic: Standing Waves |
84%
Level 1: 80%+
NEET - 2020
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