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A message signal $m(t)=\cos 2000 \pi t+4 \cos 4000 \pi t$ modulates the carrier $c(t)=\cos 2 \pi f_c t$ where $f_c=1 \; \mathrm{MHz}$ to produce an $\text{AM}$ signal. For demodulating the generated $\text{AM}$ signal using an envelope detector, the time constant $\mathrm{RC}$ of the detector circuit should satisfy

1. $0.5 \mathrm{~ms}<\mathrm{RC}<1 \mathrm{~ms}$
2. $1 \mu \mathrm{s}<<\mathrm{RC}<0.5 \mathrm{~ms}$
3. $\mathrm{RC} <<1 \mu \mathrm{s}$
4. $\mathrm{RC} >> 0.5 \mathrm{~ms}$