I made another question to it and the response was well than you get a resonant cavity!!!
Somehow Siri jumped the reading of the section where it says it’s a resonant cavity of the length is made equal to the diameter because it will have transverse modes of vibration…
I’m not sure how they changed the video or the reading of Siri to not read it!
Here is the response from the chat
Open sidebar
Resonance of Air Cylinder.
Fabio Tortorella
How thickness and length relates to the resonance of a air cylinder?
The resonance of an air cylinder depends on several factors, including its thickness and length. In general, the resonant frequency of an air cylinder is directly proportional to its length and inversely proportional to its thickness.
The resonant frequency of an air cylinder can be calculated using the formula:
f = (c/2π) x (1/L) x (A/A0)
where f is the resonant frequency, c is the speed of sound in air, L is the length of the cylinder, A is the cross-sectional area of the cylinder, and A0 is the cross-sectional area of the cylinder's neck or opening.
As you can see from the formula, the length of the cylinder is in the denominator of the equation, which means that as the length of the cylinder increases, the resonant frequency decreases. On the other hand, the thickness of the cylinder is accounted for in the cross-sectional area, which is in the numerator of the equation. Therefore, as the thickness of the cylinder increases, the resonant frequency also increases.
It's worth noting that the material and shape of the cylinder can also affect its resonant frequency, so the formula above provides only an approximation.
Fabio Tortorella
If the thickness is equal to the length does it matter?
If the thickness of an air cylinder is equal to its length, the resonant frequency of the cylinder may be affected in a different way compared to cylinders with different thickness and length ratios. In this case, the resonant frequency would be determined by other factors, such as the material and shape of the cylinder.
Generally speaking, cylinders with a length-to-thickness ratio close to one are more likely to exhibit transverse vibration modes, where the cylinder walls vibrate perpendicular to the cylinder axis. These modes are different from longitudinal modes, where the cylinder walls vibrate parallel to the cylinder axis.
In the case where the thickness is equal to the length, the cylinder is considered to be a resonant cavity, which can have complex resonant frequencies that depend on the shape and size of the cavity. The resonant frequency of the cavity can be determined by solving the wave equation for the cavity geometry, which involves taking into account the boundary conditions and the modes of vibration allowed in the cavity.
Therefore, in summary, when the thickness is equal to the length, the resonant frequency of an air cylinder can be more complex and may depend on other factors such as the shape and material of the cylinder.
Fabio Tortorella
If it was a box instead?
If we consider a rectangular box made of a material with uniform density and thickness, then its resonant frequency would depend on its dimensions, material properties, and boundary conditions.
In general, the resonant frequency of a rectangular box is determined by its fundamental modes of vibration, which depend on the length, width, and height of the box. The resonant frequency of a rectangular box can be calculated using the formula:
f = (1/2π) x sqrt(k/m) x sqrt((p/q)^2 + (q/r)^2 + (r/p)^2)
where f is the resonant frequency, k is the stiffness of the box, m is its mass, and p, q, and r are the lengths of the three sides of the box.
The resonant frequency of a box can also be affected by the boundary conditions, such as whether the box is open or closed. In general, an open box will have lower resonant frequencies than a closed box, as the open boundaries allow for greater energy dissipation and damping.
Therefore, the resonant frequency of a rectangular box will depend on its dimensions, material properties, and boundary conditions. A rectangular box can have multiple resonant frequencies, corresponding to different modes of vibration, and the resonant frequency can be determined through analysis and experimentation.
ChatGPT Feb 13 Version. Free Research Preview. Our goal is to make AI systems more natural and safe to interact with. Your feedback will help us improve.
A
