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The cutoff frequency of $TE_{01}$ mode of an air filled rectangular waveguide having inner dimensions $a\:\text{cm} \: \times \: b\: \text{cm}\:\left ( a> b \right )$ is twice that of the dominant $TE_{10}$ mode. When the waveguide is operated at a frequency which is $25\%$ higher than the cutoff frequency of the dominant mode, the guide wavelength is found to be $4\:\text{cm}$. The value of $b$ (in cm, correct to two decimal places) is ________.