Concept explainers
(a)
To identify: Whether the organ pipe is closed or open.
(a)
Answer to Problem 34P
Closed pipe.
Explanation of Solution
Given:
The frequencies = 264 Hz, 440 Hz, and 616 Hz.
Formula used:
Open pipe:
Closed pipe:
Calculation:
Open pipes resonate at frequencies f , 2f , 3f , 4f , 5f , etc.
Closed pipes resonate at frequencies f , 3f , 5f , 7f , etc.
From the given frequencies,
440Hz − 264 Hz = 176 Hz,
616 Hz − 440 Hz = 176 Hz
The given frequencies are not the multiplies of 176. Therefore, it is a closed pipe. And the fundamental frequency ff is,
The solution has odd integer. Therefore, it is closed pipe.
Conclusion:
The frequencies are in the range of odd integers. Therefore, it is a closed pipe.
(b)
The fundamental frequency of a pipe.
(b)
Answer to Problem 34P
Explanation of Solution
Given:
The frequencies = 264 Hz, 440 Hz, and 616 Hz.
Formula used:
Closed pipe:
Calculation:
Open pipes resonate at frequencies f , 2f , 3f , 4f , 5f , etc.
From the given frequencies,
440Hz − 264 Hz = 176 Hz,
616 Hz − 440 Hz = 176 Hz
The given frequencies are not the multiplies of 176. Therefore, it is a closed pipe.
Closed pipes resonate at frequencies f , 3f , 5f , 7f , etc.
And the fundamental frequency ff is,
Conclusion:
The fundamental frequency is 88 Hz, with respect to the concept of open and closed pipe principle.
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Physics: Principles with Applications
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