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(C) In $Frequency 	ext{ } Modulation$ $(FM)$, the modulation index $\beta$ is defined as $\beta = \frac{\Delta f}{f_m}$, where $\Delta f$ is the freq

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Frequency modulation

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(C) In $Frequency 	ext{ } Modulation$ $(FM)$, the modulation index $\beta$ is defined as $\beta = \frac{\Delta f}{f_m}$, where $\Delta f$ is the frequency deviation and $f_m$ is the modulating frequency.Also, the frequency deviation $\Delta f$ is directly proportional to the modulating voltage $V_m$, i.e., $\Delta f = k_f V_m$.Thus, $\beta = \frac{k_f V_m}{f_m}$.Given that the modulating voltage $V_m$ remains constant, we have $\beta \propto \frac{1}{f_m}$.If the modulating frequency $f_m$ is doubled $(f_m' = 2f_m)$, the new modulation index $\beta'$ becomes $\beta' = \frac{k_f V_m}{2f_m} = \frac{\beta}{2}$.This matches the condition given in the question, where the modulation index is halved when the frequency is doubled. Therefore, the system is $Frequency 	ext{ } Modulation$.

When the modulating frequency is doubled, the modulation index is halved and the modulating voltage remains constant, the modulation system is

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