Fundamental Resonant Frequency of a Waveguide

[HPRF]

Homework Statement

For a given rectangular waveguide the cut off frequency of the fundamental mode is 6.5GHz. What is the fundamental resonant frequency of a 30mm long cavity made from the same waveguide?

Homework Equations

Unsure

The Attempt at a Solution

I would have thought that if the rectangular waveguide dimensions didn't change then the fundamental mode would still be 6.5GHz.

I am unsure of how the length contributes to the resonant frequency...

Any help would be great.

 

[gabbagabbahey]

What are the modes of a rectangular waveguide (open on both ends w, with width $a$ and height $b$)? Which one is the fundamental mode?

What are the modes of a rectangular cavity (closed on both ends, w/ length $l=30\text{mm}$, same width and height as the previous one)? Which one is the fundamental mode?

 

[HPRF]

I'm assuming the cavity is closed at both ends as such the fundamental mode would be along the length (i.e. the 001 mode). As such using the equation derived from the dispersion relation

f=c(($$\frac{q}{2L}$$)²)^$$1/2$$

would give the fundamental frequency. With L= 30mm, q = Mode Number (1), c=Speed of Light

I think that this would be correct for a closed cavity, but is it possible of the long end is open?