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The first overtone in a closed pipe has a frequency
- a)Same as the fundamental frequency of an open tube of same length
- b)Twice the fundamental frequency of an open tube of same length
- c)Same as that of the first overtone of an open tube of same length
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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The first overtone in a closed pipe has a frequencya)Same as the funda...
Explanation:
The first overtone of a closed pipe is the second harmonic of the fundamental frequency. It means that the frequency of the first overtone is twice the frequency of the fundamental frequency.
On the other hand, the fundamental frequency of an open pipe and a closed pipe of the same length is different. The fundamental frequency of an open pipe is higher than that of a closed pipe.
Therefore, none of the options (a), (b), or (c) is correct. The correct answer is option (d), i.e., "None of the above."
To understand this concept more clearly, let's discuss the fundamental frequencies of open and closed pipes.
Fundamental Frequencies of Open and Closed Pipes:
The fundamental frequency of a pipe is given by the formula:
f = v/2L
Where,
f is the frequency of the sound wave
v is the speed of sound in the medium
L is the length of the pipe
For an open pipe, the fundamental frequency can be calculated as:
fopen = v/2L
For a closed pipe, the fundamental frequency can be calculated as:
fclosed = v/4L
It means that the fundamental frequency of an open pipe is twice the fundamental frequency of a closed pipe of the same length.
Now, let's discuss the first overtone of a closed pipe.
First Overtone of a Closed Pipe:
The first overtone of a closed pipe is the second harmonic of the fundamental frequency. It means that the frequency of the first overtone is twice the frequency of the fundamental frequency.
Therefore, the frequency of the first overtone of a closed pipe can be calculated as:
f1 = 2fclosed
f1 = 2(v/4L)
f1 = v/2L
It means that the frequency of the first overtone of a closed pipe is equal to the fundamental frequency of an open pipe of the same length.
Conclusion:
The first overtone of a closed pipe has a frequency equal to the fundamental frequency of an open pipe of the same length. Therefore, the correct answer is option (d), i.e., "None of the above."
The first overtone of a closed pipe is the second harmonic of the fundamental frequency. It means that the frequency of the first overtone is twice the frequency of the fundamental frequency.
On the other hand, the fundamental frequency of an open pipe and a closed pipe of the same length is different. The fundamental frequency of an open pipe is higher than that of a closed pipe.
Therefore, none of the options (a), (b), or (c) is correct. The correct answer is option (d), i.e., "None of the above."
To understand this concept more clearly, let's discuss the fundamental frequencies of open and closed pipes.
Fundamental Frequencies of Open and Closed Pipes:
The fundamental frequency of a pipe is given by the formula:
f = v/2L
Where,
f is the frequency of the sound wave
v is the speed of sound in the medium
L is the length of the pipe
For an open pipe, the fundamental frequency can be calculated as:
fopen = v/2L
For a closed pipe, the fundamental frequency can be calculated as:
fclosed = v/4L
It means that the fundamental frequency of an open pipe is twice the fundamental frequency of a closed pipe of the same length.
Now, let's discuss the first overtone of a closed pipe.
First Overtone of a Closed Pipe:
The first overtone of a closed pipe is the second harmonic of the fundamental frequency. It means that the frequency of the first overtone is twice the frequency of the fundamental frequency.
Therefore, the frequency of the first overtone of a closed pipe can be calculated as:
f1 = 2fclosed
f1 = 2(v/4L)
f1 = v/2L
It means that the frequency of the first overtone of a closed pipe is equal to the fundamental frequency of an open pipe of the same length.
Conclusion:
The first overtone of a closed pipe has a frequency equal to the fundamental frequency of an open pipe of the same length. Therefore, the correct answer is option (d), i.e., "None of the above."
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The first overtone in a closed pipe has a frequencya)Same as the fundamental frequency of an open tube of same lengthb)Twice the fundamental frequency of an open tube of same lengthc)Same as that of the first overtone of an open tube of same lengthd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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