Here we consider the interference between two harmonic waves at t0 (a- 1pt) using matlab produce a plot of (x,に0) according to eq. (1) on the interval a-p.30] for kı-2, k2-1.8 b - 2pts) by using the rules for the sum of trigonometric functions show that (x, t-0) 2 cos k+ with k± = (kit k2)/2 > 0. the interference of the two waves can therefore be expressed as a product of cosine functions with different propagation numbers il. hint: to apply one of the commonly listed sum-to-product trig identities, you may want to express sin(k2r) in term of cos function with a shifted argument c- 2pts) for ki k2 the average propagation number k+(k+ k2)/2 ki controls the fast carrier oscilations that arise in your plot from part (a), whereas the "spread" k- -(ki - k2)/2 < < k+ describes the slower spatial envelope that modulates the carrier oscillation. the spatial periods l+ of the carrier and envelope fringes follow from the relations k± 2π, which requires the harmonic waves to repeat in phase after a period. demonstrate that the spatial periods l+ ~ 2π/h and l-~ 4n/(ki-k2) indeed appear in your numerical results from part (a)

What is the role of the ocular lens?

Aroll in a paper machine is powered by a separately excited dc machine. operating point 1 (under load): the roll typically operates at 764 rpm and must provide 301 nm of torque to oppose the load of the paper. the armature voltage is 230v for this operating point operating point 2 (no load): when the load is removed the speed of the roll increases to 900 rpm (the field characteristics are unchanged) la ea dev m (a) calculate the maximum torque (units of nm) that the motor can supply with this applied voltage (b) calculate the value of the armature resistance, ra (in ohms) (c) at operating point 1 (loaded condition), the field current, i, and the total input power (armature field), are measured to be to be 10 a and 28,600 w respectively. use this information to calculate the value of the field resistance, rf (in ohms). (d) (d) at operating point 1 (loaded condition), calculate the motor efficiency. express your answer as a percent to at least 2 significant digits. (d) if the field voltage is reduced by 1/2, calculate the new stall torque (in nm) of the motor (f). if the field voltage is reduced by 1/2, calculate the new no-load speed (in rad/sec)

Which of the following is not a part of the respiratory system? a. pharynx b. trachea c. pancreas d. larynx