## EMC Question of the Week: June 7, 2021

The first (lowest) resonant frequency of a 40-cm x 16-cm x 38-cm rectangular metal enclosure is

- below 10 MHz
- approximately 380 MHz
- approximately 540 MHz
- above 1 GHz

## Answer

The best answer is “c.” The resonance frequencies of an air-filled rectangular metal enclosure are given by the expression,

$${f}_{mnp}=\frac{c}{2}\sqrt{{\left(\frac{m}{a}\right)}^{2}+{\left(\frac{n}{b}\right)}^{2}+{\left(\frac{p}{d}\right)}^{2}}$$where a, b and d are the dimensions of the enclosure; c is the propagation velocity; and m, n and p are non-negative integers (at least two of them non-zero). The assignment of dimensions corresponding to a, b and d is arbitrary, but for a<b<d the lowest resonant frequency is f_{011}. For this enclosure,

Of course, we have assumed that the question is asking about the first electromagnetic (not acoustic) resonance, and that the enclosure is mostly empty (e.g., not filled with a dielectric).

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