The equation of a stationary wave is given as $\mathrm{y}=\mathrm{A}$ $\mathrm{sin}$ $0.5\mathrm{\pi t}$ $\mathrm{cos}\left(0.2\mathrm{\pi x}\right),$  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 |
89%
From NCERT
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A standing wave is represented by $Y=A\mathrm{sin}\left(100t\right)\mathrm{cos}\left(0.01x\right)$ 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. $\frac{1}{n}=\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}+\frac{1}{{n}_{3}}$

2. $n={n}_{1}×{n}_{2}×{n}_{3}$

3. $n={n}_{1}+{n}_{2}+{n}_{3}$

4. $n=\frac{{n}_{1}+{n}_{2}+{n}_{3}}{3}$

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%
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:  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%
From NCERT
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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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