b
આપેલ \(AM\) તરંગ \(e = 50 (1 + 0.5 \,sin\, (2\pi × 5 ×10^{3}) t) \,sin\, (31.4 × 10^{6}) t \) ને \(e = E_c (1 + m_a \,\,sin\,\, w_mt) \,\,sin\,\, w_ct\, \) સાથે સરખાવતાં, \(w_m = 2\pi × 5 × 10^{3} rad/s\)

માડ્યુલેટિંગ તરંગની આવૃત્તિ, \({{f}_m}\,\, = \,\,\frac{{{\omega _m}}}{{2\pi }}\,\, = \,\,\frac{{2\pi \,\, \times \,5\,\, \times \,\,{{10}^3}}}{{2\pi }}\,\, = \,\,5\,\,kHz\)

હવે,\(wc = 31.4 × 10^6 rad/s\)

કેરિયર તરંગની આવૃત્તિ,  \({{f}_c}\,\, = \,\frac{{{\omega _c}}}{{2\pi }}\,\, = \,\,\frac{{31.4\,\, \times \,\,{{10}^6}}}{{2\,\, \times \,\,3.14}}\,\, = \,\,5\,\, \times \,\,{10^6}\,\,\, = \,\,5\,\,MHz\)