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A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then, the number of beats produced per second while vibrating in the fundamental mode is___
  • a)
    8
  • b)
    7
  • c)
    2
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?
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A closed organ pipe and an open organ pipe of same length produce 2 be...
Understanding the Initial Conditions
The problem begins with a closed organ pipe and an open organ pipe of the same length. They produce 2 beats per second in their fundamental modes.
Fundamental Frequencies of Pipes
- The frequency of a closed organ pipe (F_closed) is given by the formula:
F_closed = v / 4L
- The frequency of an open organ pipe (F_open) is given by the formula:
F_open = v / 2L
Here, "v" is the speed of sound, and "L" is the length of the pipe.
Initial Frequencies and Beat Frequency
- Since the pipes produce 2 beats per second:
|F_closed - F_open| = 2 Hz
Adjusting the Lengths of the Pipes
- The length of the open organ pipe is halved:
New length (L_open) = L/2
- The length of the closed organ pipe is doubled:
New length (L_closed) = 2L
New Frequencies After Adjustments
- New frequency of the closed pipe (F_closed_new):
F_closed_new = v / 4(2L) = v / 8L
- New frequency of the open pipe (F_open_new):
F_open_new = v / 2(L/2) = v / L
Calculating the New Beat Frequency
- The new beat frequency is calculated as:
|F_closed_new - F_open_new| = |(v / 8L) - (v / L)|
- Simplifying this gives:
|F_closed_new - F_open_new| = |(v - 8v) / 8L| = 7v / 8L
Thus, the beat frequency = 7 beats/second.
Conclusion
The number of beats produced per second while vibrating in the fundamental mode after the changes is 7 beats/second, confirming that the correct answer is option 'B'.
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A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then, the number of beats produced per second while vibrating in the fundamental mode is___a)8b)7c)2d)6Correct answer is option 'B'. Can you explain this answer?
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A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then, the number of beats produced per second while vibrating in the fundamental mode is___a)8b)7c)2d)6Correct answer is option 'B'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then, the number of beats produced per second while vibrating in the fundamental mode is___a)8b)7c)2d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then, the number of beats produced per second while vibrating in the fundamental mode is___a)8b)7c)2d)6Correct answer is option 'B'. Can you explain this answer?.
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