When modulation frequency is doubled modulation index also doubled in case of FM or pm or am?

In Frequency Modulation (FM), if the modulation frequency is doubled, the modulation index does not necessarily double; it depends on the amplitude of the modulating signal. In Amplitude Modulation (AM), the modulation index is defined as the ratio of the peak amplitude of the modulating signal to the carrier amplitude, so it remains unchanged with varying modulation frequency. For Phase Modulation (PM), similar to FM, the modulation index is influenced by the amplitude of the modulating signal and does not inherently double with the modulation frequency. Thus, modulation frequency and modulation index are not directly linked in this way for FM, PM, or AM.