An important use of waveguide theory is in the design of shielded rooms. These rooms are used to isolate sensitive equipment and experiments from the effects of external electromagnetic fields, as well as to prevent the radiation from the equipment in the room from reaching the external environment. However, the room cannot be a continuous enclosure since air vents must penetrate the walls so that personnel can operate the test equipment in the room. In order to restrict electromagnetic penetration through these vents while allowing airflow, a "honeycomb" structure is inserted into the vent. This consists of a large number of small, rectangular tubes which are welded together. Each tube may be viewed as a waveguide. The intent is for these tubes to operate as a "waveguide below cutoff" in restricting penetration of external and internal fields. If the cross-section of each tube of the vent structure is square with dimensions 0.5 by 0.5 cm, determine the range of frequencies that are excluded by the structure.

As a continuation of the above problem, assume that the length of the vent tubes (in the direction perpendicular to the wall) is 5.0 cm. Calculate the dB of attenuation going through the vent for a wave at 1.0 GHz, basing your answer on the dominant TE10 mode.