A DSB-SC modulated signal is demodulated by applying it to a coherent detector. (a) Evaluate the effect of a frequency error !J. f in the local carrier frequency of the detector, measured with respect to the carrier frequency of the incoming DSB-SC signal. (b) For the case of a sinusoidal modulating wave, show that because of this frequency error, the demodulated signal exhibits beats at the error frequency. Illustrate your answer with a sketch of this demodulated signal.

Steam in a heating system flows through tubes whose outer radius is 2.5 cm and whose walls are maintained at a temperature of 180 °c . circular aluminum alloy 2024-t6 fins ( k= 186 wm. k) of outer radius 3 cm and constant thickness 1 mm are attached to the tube. the space between the fins is 3 mm and thus there are 250 fins per meter of tube length. heat is transferred to the surrounding air at too-25 °c, with a heat transfer coefficient of 40 w/m2. k. manufacturer a claims that this system is rated at 3.5 kw per meter of tube length. if the fins are an integral part of the steam tube, find the heat transfer rate in kw for a 1-m length of tube. is manufacturer a's claim valid? compare the heat transfer rate from 1 meter of tube length if there are no fins.