# Resonant Frequencies of Coaxial Cylinders

## Main Question or Discussion Point

Does anyone know of a formula for determining the various resonant frequencies of 2 coaxial cylinders with radius a and b and height h? Thanks.

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well the resonant frequency is basically determined by the length of the tube (cyclinder). In closed end cyclinders the resonant frequency has a wave length of four times the length of the cylinder. In order to get it resonating required a wave of enough amplitude (energy) to make it resonate.

Similarly the resonant wave length in an open ended cylinder is double the length of the cyclinder

I appreciate that, but my question pertains to two cylinders, on inside the other. I need to find the resonant frequency of the cavity between them. I have the formula for a single cylinder, but can not find one for the coaxial set.

First, I assume you have a connector on one end. What kind of connector, and what is the impedance of the connecting cable? 50 ohms? 75 ohms

Second, is the other end of the coaxial tube assembly open or shorted?

third, the impedance of the coaxial tube assembly is

Z = [377/(2 pi)] Ln(b/a) where b is the radius of the larger cylinder.

Fourth, the one-way transit time is h/c where c= 3 x 108 meters per sec. h is the full wave wavelength. The full wave frequency is c/h. The lowest resonant frequency is the 1/4 wave frequency, c/4h. If one end is open, the other looks like a short. If one end is shorted, the other end should have an impedance Z2/(short resistance). A quarter wave line is an impedance transformer. If the Z of the coaxial tube is not the same as the impedance of the cable, then you have an impedance mismatch. See attached thumbnail for a 0 to 100 MHz frequency sweep of a 10-ns long coaxial 50 ohm line. The 10-ns line looks open at the 1/4 and 3/4 wavelength frequencies (25 and 75 MHz), and shorted at the 1/2 and 1/1 (50 and 100 MHz) wavelength frequencies

 Here is a website for quarter wave lines referred by Berkman
http://www.microwaves101.com/encyclopedia/quarterwave.cfm

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