The frequency which, under the sampling theorem, must be exceeded by the sam- pling frequency is called the Nyquist rate. Determine the Nyquist rate corresponding to each of the following signals:

a. x(t) = 1 + cos(2000 pi t) + sin (4000 pi t)
b. x(t) = sin (500 pi t)/pi t

Air is to be cooled in the evaporator section of a refrigerator by passing it over a bank of 0.8-cm-outer-diameter and 0.4-m-long tubes inside which the refrigerant is evaporating at -20°c. air approaches the tube bank in the normal direction at 0°c and 1 atm with a mean velocity of 4 m/s. the tubes are arranged in-line with longitudinal and transverse pitches of sl- st 1.5 cm. there are 30 rows in the flow direction with 15 tubes in each row. determine (a) the refrigeration capacity of this system and (b) pressure drop across the tube bank. evaluate the air properties at an assumed mean temperature of -5°c and 1 atm. is this a good assumption?