• # question_answer A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are : [JEE Main 10-4-2019 Morning] A) $4;1\times {{10}^{8}}Hz$             B) $0.25;1\times {{10}^{8}}Hz$C) $4;2\times {{10}^{8}}Hz$             D) $0.25;\,2\times {{10}^{8}}Hz$

${{f}_{m}}=100MHz={{10}^{8}}Hz,$${{({{V}_{m}})}_{0}}=100V$           ${{f}_{c}}=300GHz$                $,{{({{V}_{c}})}_{0}}=400V$ Modulaton Index $=\frac{{{({{V}_{m}})}_{0}}}{{{({{V}_{c}})}_{0}}}=\frac{100}{400}=\frac{1}{4}=0.25$ Upper band frequency (UBF) $={{f}_{c}}+{{f}_{m}}$ Lower band frequency (LBF) $={{f}_{c}}-{{f}_{m}}$ $\therefore UBF-LBF=2{{f}_{m}}=2\times {{10}^{8}}Hz$