Q. No.The equation of a stationary wave is given as \(y =A\sin(0.5\pi t)\cos(0.2\pi x)\) where \(t\) is in seconds and \(x\) in centimetres. Which of the following is correct?
| 1. | Wavelength of the component waves is \(10~\text{cm}.\) |
| 2. | The separation between a node and the nearest antinode is \(2.5~\text{cm}.\) |
| 3. | Frequency of the component wave is \(0.25~\text{Hz}\). |
| 4. | All of these |
Subtopic: Â Standing Waves |
 89%
From NCERT
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The equation of vibration of a taut string, fixed at both ends, is given by:
\(y=(3~\text{mm})~\text{cos}\Big(\frac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
The speed of waves on the string is:
1. \(20\) m/s
2. 40 m/s
3. \(80\) m/s
4. \(160\) m/s
\(y=(3~\text{mm})~\text{cos}\Big(\frac{\pi x}{10~\text{cm}}\Big)~\text{sin}(800\pi~\text{s}^{-1}~\text{t})\)
The speed of waves on the string is:
1. \(20\) m/s
2. 40 m/s
3. \(80\) m/s
4. \(160\) m/s
Subtopic: Â Standing Waves |
 90%
From NCERT
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A standing wave is represented by \(y = A\sin(100t)\cos(0.01x)\) where \(y\) and \(A\) are in millimetres, \(t\) is in seconds and \(x\) is in metres. The velocity of the wave is:
| 1. | \(10^{4}~\text{m/s}\) |
| 2. | \(1~\text{m/s}\) |
| 3. | \(10^{-4}~\text{m/s}\) |
| 4. | Not derivable from the above data |
Subtopic: Â Standing Waves |
 87%
From NCERT
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A string is cut into three parts, having fundamental frequencies \(n_1,n_2,\) and \(n_3\) respectively. The original fundamental frequency \(n\) is related by the expression:
1. \(\frac{1}{n}= \frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\)
2. \(n= n_1\times n_2\times n_3\)
3. \(n= n_1+ n_2+ n_3\)
4. \(n= \frac{n_1+ n_2+ n_3}{3}\)
1. \(\frac{1}{n}= \frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}\)
2. \(n= n_1\times n_2\times n_3\)
3. \(n= n_1+ n_2+ n_3\)
4. \(n= \frac{n_1+ n_2+ n_3}{3}\)
Subtopic: Â Standing Waves |
 85%
From NCERT
AIPMT - 2000
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A string of length \(l\) is fixed at one end and free at the other. If it resonates in different modes, then the ratio of frequencies is:
1. \(1:2:3:~.......\)
2. \(1:3:5:7~.......\)
3. \(1:2:4:8~.......\)
4. \(1:3:9:~.......\)
1. \(1:2:3:~.......\)
2. \(1:3:5:7~.......\)
3. \(1:2:4:8~.......\)
4. \(1:3:9:~.......\)
Subtopic: Â Standing Waves |
 82%
From NCERT
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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: Â Standing Waves |
 82%
From NCERT
NEET - 2020
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The fundamental frequency of an open organ pipe is \(200~\text{Hz}\). If one end of the pipe is closed, its fundamental frequency becomes:
| 1. | \(100~\text{Hz}\) | 2. | \(200~\text{Hz}\) |
| 3. | \(50~\text{Hz}\) | 4. | \(400~\text{Hz}\) |
Subtopic: Â Standing Waves |
 80%
From NCERT
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An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is \(50~\text{cm}\). The next larger length of the column resonating with the same tuning fork will be:
| 1. | \(100~\text{cm}\) | 2. | \(150~\text{cm}\) |
| 3. | \(200~\text{cm}\) | 4. | \(66.7~\text{cm}\) |
Subtopic: Â Standing Waves |
 79%
From NCERT
NEET - 2016
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The equation of a stationary wave is \(y = 0.8\cos\left(\frac{\pi x}{20}\right)\sin200(\pi t)\), where \(x\) is in cm and \(t\) is in sec. The separation between consecutive nodes will be:
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(40~\text{cm}\)
4. \(30~\text{cm}\)
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(40~\text{cm}\)
4. \(30~\text{cm}\)
Subtopic: Â Standing Waves |
 77%
From NCERT
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If a standing wave having \(3\) nodes and \(2\) antinodes is formed within \(1.21~\mathring{A}\) distance, then the wavelength of the standing wave will be:
1. \(1.21~\mathring{A}\)
2. \(2.42~\mathring{A}\)
3. \(0.605~\mathring{A}\)
4. \(4.84~\mathring{A}\)
1. \(1.21~\mathring{A}\)
2. \(2.42~\mathring{A}\)
3. \(0.605~\mathring{A}\)
4. \(4.84~\mathring{A}\)
Subtopic: Â Standing Waves |
 79%
From NCERT
AIPMT - 1998
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