The equation of a stationary wave is given as y=A sin 0.5πt cos(0.2πx),  where t is in seconds and x in centimetres. Which of the following is correct?

1. Wavelength of the component waves is 10 cm.
2. The separation between a node and the nearest antinode is 2.5 cm.
3. Frequency of the component wave is 0.25 Hz.
4. All of these

Subtopic:  Standing Waves |
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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
Subtopic:  Standing Waves |
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From NCERT
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A standing wave is represented by Y=Asin(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. 104 m/s
2. 1 m/s
3. 10–4 m/s
4. Not derivable from the above data

Subtopic:  Standing Waves |
 87%
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A string is cut into three parts, having fundamental frequencies n1, n2, and nrespectively. The original fundamental frequency "n" is related by the expression:

1. 1n=1n1+1n2+1n3

2. n=n1×n2×n3

3. n=n1+n2+n3

4. n=n1+n2+n33

Subtopic:  Standing Waves |
 84%
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: ........

Subtopic:  Standing Waves |
 82%
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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 |
 82%
From NCERT
NEET - 2020
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The fundamental frequency of an open organ pipe is 200 Hz. If one end of the pipe is closed, its fundamental frequency becomes:

1. 100 Hz 2. 200 Hz
3. 50 Hz 4. 400 Hz
Subtopic:  Standing Waves |
 80%
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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 \(50\) cm. The next larger length of the column resonating with the same tuning fork will be:

1. \(100\) cm 2. \(150\) cm
3. \(200\) cm 4. \(66.7\) cm
Subtopic:  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. \(30~\text{cm}\)

Subtopic:  Standing Waves |
 76%
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If a standing wave having 3 nodes and 2 antinodes is formed within 1.21 Å distance, then the wavelength of the standing wave will be:
1. 1.21 Å
2. 2.42 Å
3. 0.605 Å
4. 4.84 Å

Subtopic:  Standing Waves |
 78%
From NCERT
AIPMT - 1998
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