Answer – 9V

Explanation –

We are given –

Amplitude of carrier wave ; \[{{A}_{c}}\]  = 12 V

Modulation index (m) = 75% = 0.75

Amplitude of the modulating wave = ${{A}_{m}}$

We will now use the formula of modulation index, given by –

  $$ m=\frac{{{A}_{m}}}{{{A}_{c}}} $$

 $$ \therefore {{A}_{m}}=m{{A}_{c}} $$

 $$ {{A}_{m}}=0.75\times 12 $$

 $$ {{A}_{m}}=9V $$

Therefore, 9V should be the peak voltage of the modulating signal in order to have a modulation index of 75%.