Given below are two statements:
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.
In the light of the above statements, choose the correct answer from the options given below:
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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The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is:
1. \(3:1\) 2. \(1:2\)
3. \(2:1\) 4. \(1:3\)
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The \(4^\mathrm{th}\) overtone of a closed organ pipe is the same as that of the \(3^\mathrm{rd}\) overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
1. \(8:9\)     2. \(9:7\)    
3. \(9:8\) 4. \(7:9\)
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A string of length \(l\) is fixed at both ends and is vibrating in second harmonic. The amplitude at antinode is \(2\) mm. The amplitude of a particle at a distance \(l/8\) from the fixed end is:
        
1. \(2\sqrt2~\text{mm}\)
2. \(4~\text{mm}\)
3. \(\sqrt2~\text{mm}\)
4. \(2\sqrt3~\text{mm}\)

Subtopic:  Standing Waves |
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An organ pipe filled with a gas at \(27^\circ \text{C}\) resonates at \(400\) Hz in its fundamental mode. If it is filled with the same gas at \(90^\circ \text{C},\) the resonance frequency at the same mode will be:
1. \(420\) Hz 2. \(440\) Hz
3. \(484\) Hz 4. \(512\) Hz
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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
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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is \(20~\text{cm}\), the length of the open organ pipe is:
1. \(13.2~\text{cm}\)
2. \(8~\text{cm}\)
3. \(12.5~\text{cm}\)
4. \(16~\text{cm}\)

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The two nearest harmonics of a tube closed at one end and open at the other end are \(220\) Hz and \(260\) Hz. What is the fundamental frequency of the system? 
1. \(20\) Hz
2. \(30\) Hz
3. \(40\) Hz
4. \(10\) Hz

 
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The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe \(L\) meter long. The length of the open pipe will be:
1. \(L\)
2. \(2L\)
3. \(\frac{L}{2}\)
4. \(4L\)

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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. \(66.7~\text{cm}\)
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