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An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is (in Hz) ____.
Correct answer is '200'. Can you explain this answer?
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Explanation:
To understand this problem, let's break it down step by step.
Step 1: Understanding the concept of harmonics
- Harmonics are multiples of the fundamental frequency of a vibrating object or a resonant system.
- In the case of a pipe, the fundamental frequency is the frequency at which the pipe resonates with its maximum amplitude.
- The second harmonic is twice the frequency of the fundamental, the third harmonic is three times the frequency, and so on.
Step 2: Understanding the difference between an open pipe and a closed pipe
- An open pipe, as the name suggests, is open at both ends. This allows air to move freely in and out of the pipe.
- A closed pipe, on the other hand, is closed at one end. This means that air is unable to escape from that end.
Step 3: Analyzing the problem
- In this problem, we are given that an open pipe suddenly closes at one end.
- When the pipe was open, its fundamental frequency was f.
- Now, after closing the pipe, we observe that the frequency of the third harmonic of the closed pipe is higher by 100 Hz than the fundamental frequency of the open pipe.
Step 4: Applying the concept of harmonics
- Let's assume that the fundamental frequency of the open pipe is f. This means that the frequency of the third harmonic of the open pipe would be 3f.
- According to the problem, the frequency of the third harmonic of the closed pipe is 3f + 100 Hz.
- Since the pipe is closed at one end, the closed pipe can only have odd harmonics (1st, 3rd, 5th, etc.). Therefore, we can conclude that the fundamental frequency of the closed pipe is 3f + 100 Hz.
Step 5: Solving the problem
- We know that the fundamental frequency of the closed pipe is 3f + 100 Hz.
- We are also given that the frequency of the third harmonic of the closed pipe is 3f + 100 Hz.
- Equating these two frequencies, we get:
3f + 100 Hz = 3f
100 Hz = 2f
f = 50 Hz
Therefore, the fundamental frequency of the open pipe is 50 Hz.
To understand this problem, let's break it down step by step.
Step 1: Understanding the concept of harmonics
- Harmonics are multiples of the fundamental frequency of a vibrating object or a resonant system.
- In the case of a pipe, the fundamental frequency is the frequency at which the pipe resonates with its maximum amplitude.
- The second harmonic is twice the frequency of the fundamental, the third harmonic is three times the frequency, and so on.
Step 2: Understanding the difference between an open pipe and a closed pipe
- An open pipe, as the name suggests, is open at both ends. This allows air to move freely in and out of the pipe.
- A closed pipe, on the other hand, is closed at one end. This means that air is unable to escape from that end.
Step 3: Analyzing the problem
- In this problem, we are given that an open pipe suddenly closes at one end.
- When the pipe was open, its fundamental frequency was f.
- Now, after closing the pipe, we observe that the frequency of the third harmonic of the closed pipe is higher by 100 Hz than the fundamental frequency of the open pipe.
Step 4: Applying the concept of harmonics
- Let's assume that the fundamental frequency of the open pipe is f. This means that the frequency of the third harmonic of the open pipe would be 3f.
- According to the problem, the frequency of the third harmonic of the closed pipe is 3f + 100 Hz.
- Since the pipe is closed at one end, the closed pipe can only have odd harmonics (1st, 3rd, 5th, etc.). Therefore, we can conclude that the fundamental frequency of the closed pipe is 3f + 100 Hz.
Step 5: Solving the problem
- We know that the fundamental frequency of the closed pipe is 3f + 100 Hz.
- We are also given that the frequency of the third harmonic of the closed pipe is 3f + 100 Hz.
- Equating these two frequencies, we get:
3f + 100 Hz = 3f
100 Hz = 2f
f = 50 Hz
Therefore, the fundamental frequency of the open pipe is 50 Hz.
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An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is (in Hz) ____.Correct answer is '200'. Can you explain this answer?
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