Diameter and Fundamental Frequency

In summary, the question asks for the fundamental frequencies of two open tubes with lengths of 1m and diameters of 1cm and 10cm, taking into account end corrections. The attempted solution involved using an equation for critical mode and the frequency formula, but did not yield the correct answer. Further research on the frequency of open organ pipes as a function of pipe diameter end correction may be needed.
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mtreichl
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Homework Statement


Two open tubes both have actual length 1m but their diameters are D=1 cm and D=10 cm. Alowing fro end corrections, what are their fundamental frequencies?


Homework Equations



the only equation in my book that deals with Diamter is N(Critical Mode)=L(Length)/D(Diameter) I tried using this to find a mode to plug into f=nV/2L but that did not get me the right answer.

The Attempt at a Solution

 
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1. What is the relationship between diameter and fundamental frequency?

The diameter of an object is directly proportional to its fundamental frequency. This means that as the diameter increases, the fundamental frequency also increases. Additionally, a change in diameter will result in a change in the wavelength of the sound produced.

2. How does the diameter of an object affect its sound?

The diameter of an object affects its sound by determining the fundamental frequency of the sound wave it produces. A larger diameter will result in a lower fundamental frequency and a deeper sound, while a smaller diameter will result in a higher fundamental frequency and a higher-pitched sound.

3. How is the diameter of a string related to its fundamental frequency?

The diameter of a string is directly proportional to its fundamental frequency. This means that as the diameter of a string increases, the fundamental frequency decreases, resulting in a lower pitch. Similarly, as the diameter decreases, the fundamental frequency increases, producing a higher pitch.

4. Can the diameter of an object affect its harmonics?

Yes, the diameter of an object can affect its harmonics. As the diameter increases, the harmonics of an object will also increase, resulting in a richer and more complex sound. A smaller diameter will produce fewer harmonics and a simpler sound.

5. How does the diameter of an object relate to its resonance?

The diameter of an object is directly related to its resonance. Objects with larger diameters will have lower resonant frequencies, while objects with smaller diameters will have higher resonant frequencies. This is because the diameter determines the fundamental frequency of an object, which is also the resonant frequency.

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