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Standard air-filled rectangular waveguides of dimensions $a=2.29$ cm and $b=1.02 $ cm are designed for radar applications. It is desired that these waveguides operate only in the dominant $TE_{10}$ mode with the operating frequency at least $25 \%$ above the cutoff frequency of the $TE_{10}$ mode but not higher than $95 \%$ of the next higher cutoff frequency. The range of the allowable operating frequency $f$ is 

  1. $8.19 \: GHz \leq f \leq 13.1 \:GHz$
  2. $8.19 \: GHz \leq f \leq 12.45 \: GHz$
  3. $6.55 \: GHz \leq  f \leq 13.1 \: GHz$
  4. $1.64 \: GHz \leq f \leq 10.24 \: GHz$
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