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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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 |
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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 |
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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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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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A string of length 3 m and a linear mass density of 0.0025 kg/m is fixed at both ends. One of its resonance frequencies is 252 Hz. The next higher resonance frequency is 336 Hz. Then the fundamental frequency will be:
1. 84 Hz

2. 63 Hz

3. 126 Hz

4. 168 Hz

Subtopic:  Standing Waves |
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The fundamental frequency of a closed organ pipe of a length $$20$$ cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

 1 $$80$$ cm 2 $$100$$ cm 3 $$120$$ cm 4 $$140$$ cm
Subtopic:  Standing Waves |
77%
From NCERT
NEET - 2015
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In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. If the tension of the string remains constant, then the frequency of the second tuning fork will be:

1. 163.84 Hz

2. 400 Hz

3. 320 Hz

4. 204.8 Hz

Subtopic:  Standing Waves |
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A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for these strings is:

 1 155 Hz 2 205  Hz 3 10.5 Hz 4 105  Hz
Subtopic:  Standing Waves |
76%
From NCERT
NEET - 2015
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A closed pipe and an open pipe have their first overtones identical in frequency. Their lengths are in the ratio:

 1 1 : 2 2 2 : 3 3 3 : 4 4 4 : 5
Subtopic:  Standing Waves |
73%
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