Formula relating thickness of pipe to fundamental frequency

[Zoro]

Homework Statement

I understand how to find the resonant frequency of a closed pipe but when the thickness of the walls varies, the resonant frequency varies. Is there a formula that i can use to find the resonant frequency of a closed pipe given the length, temperature, speed of sound and THICKNESS. Thank you for any help :)

Homework Equations

The Attempt at a Solution

I attempted a few experiments in which i used a technique called over blowing but i also want to calculate it mathematically if possible.

 

[haruspex]

I was not aware that the wall thickness does affect the fundamental frequency of the notes produced by the column of air. I can understand how it alters any notes generated by vibration of the pipe walls, and how it may attenuate different harmonics from the air column differently. Both of those will make the note sound different, but the fundamental frequency should be the same.
Maybe someone else knows some subtleties I'm missing.

 

[nasu]

Yes, are talking about modes of the air in the tube or about the flexural modes of the pipe?

 

[Zoro]

i mean the resonant frequency. Basically i was trying to determine the resonant frequency of a closed pipe (measuring cylinder) and looked at different cylinders with different thicknesses of the walls. I used a technique called over blowing

 

[nasu]

Both types of vibrations (air vibration and wall vibration) have resonant frequencies.
How did you measure the frequency?
By over blowing you mean a technique of exciting higher modes of a wind instrument?

 

[Zoro]

By overblowing, i mean i hit the glass measuring cylinder twice with my finger and then blew air over the opening. The sound that was made was recorded and the natural / resonant frequency was calculated using f = waves/ time

 

[Nidum]

The cylinder itself has natural frequencies of vibration - these are what you excite when you tap the cylinder . During vibration the cylinder flexes in the same way as a bell does - hence this type of vibration is commonly called bell mode vibration .

The air column in the cylinder has a different set of natural frequencies - these are what you excite when you blow over the cylinder .

The level of interaction between bell mode vibration and air column vibration has to be investigated case by case but very often the interaction is so weak that the two can be looked at individually .

If you tap the cylinder quite sharply with a metal spoon or similar you will clearly hear the bell mode vibrations . Usually quite a clear musical note is produced .

The material and geometry of the cylinder determine its natural frequencies .

 

[SammyS]

By overblowing, i mean i hit the glass measuring cylinder twice with my finger and then blew air over the opening. The sound that was made was recorded and the natural / resonant frequency was calculated using f = waves/ time

Over-blowing generally produces some harmonic, not the fundamental frequency.

Were the various resonant frequencies you obtained approximately a multiple of the fundamental frequency?