# Understanding Harmonics and Overtones in Closed and Open Pipe Organ Designs

• SeanGillespie
In summary, there is a discrepancy between the lecturer's notes and the textbook regarding the labeling of harmonics for a closed-ended organ pipe. The lecturer's notes state that the 1st, 2nd, and 3rd harmonics correspond to frequencies of 4L, 4L/3, and 4L/5 respectively. However, the textbook labels these as the 1st, 3rd, and 5th harmonics. It is possible that the lecturer was referring to overtones rather than harmonics.
SeanGillespie
This isn't actually a homework/coursework question, but rather a need to clarify a discepancy between my lecturer's notes and a textbook.

My lecturer's notes state that for an "organ" pipe, closed at one end, the 1st harmonic frequency will be 4L. For the 2nd harmonic the frequency will be 4L/3. And for the 3rd harmonic the frequency will be 4L/5. (Where L is the length of the organ pipe)

However, in my textbook it denotes these same frequencies as the 1st, 3rd and 5th harmonic, rather than 1st, 2nd and 3rd. Which is the correct formula? My lecturer's or my textbook's? (see attached image from textbook)

--- Sorry, correction: I meant wavelength in all above cases, not frequency. ---

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• instrument harmonics.PNG
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Hello sean.With the closed end pipe you get odd harmonics only but with the open ended pipe you get odd and even harmonics.I suspect your lecturer was referring to overtones rather than harmonics.

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## 1. What is a closed pipe harmonic?

A closed pipe harmonic is a type of sound wave that is produced in a pipe that is closed at one end and open at the other. This type of sound wave is characterized by having a node at the closed end and an antinode at the open end.

## 2. How is a closed pipe harmonic different from an open pipe harmonic?

A closed pipe harmonic is different from an open pipe harmonic in terms of the location of the nodes and antinodes. In a closed pipe, the node is at the closed end and the antinode is at the open end, whereas in an open pipe, both ends are antinodes.

## 3. What factors affect the frequency of a closed pipe harmonic?

The frequency of a closed pipe harmonic is affected by the length of the pipe, the speed of sound in the medium, and the temperature of the medium. The longer the pipe, the lower the frequency, and the higher the speed of sound or temperature, the higher the frequency.

## 4. What is the relationship between the harmonics in a closed pipe?

The harmonics in a closed pipe are related by a simple mathematical ratio. The fundamental frequency (first harmonic) is half of the length of the pipe, and each subsequent harmonic is an integer multiple of the fundamental frequency.

## 5. How is the sound produced in a closed pipe harmonic?

The sound in a closed pipe harmonic is produced by the vibration of the air inside the pipe. When the air is set into motion by a sound source, such as a vibrating string or a person's voice, it travels down the pipe and reflects off the closed end, creating the characteristic wave pattern.

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