y doping semiconductors, it is possible to create materials with specifically d lectromagnetic properties for waves propagating within them. The following 1-D plan t a frequency of 10THz propagates in a heavily n-doped silicon: Ē = E ejot = Ēejot ē jat-jyz - t this frequency and the doping level, the conductivity of the medium is o = 105 Sm ave loses 3 dB of intensity (power) over a length of 184 nm. Assume the permittivity edium is purely real. Find the amplitude attenuation constant, a . the relative permittivity of the medium, &,

Give the peak value, angluar velocity (w), frequency (f), and period (T) for ac wave i=4.0sin 120πt

Imagine a two-dimensional system in which a sinusoidal waveform is excited at the exact center of a circular plate. The standing wave pattern is established when the excited wave two-dimensionalwaveforms for a stable equilibrium pattern of constructive and destructive interference with the reflected waves from the edge of the circular plate. Draw what you expect the standing wave patterns to look like in this two-dimensional system for increasing resonant harmonics, n. Explain what characteristics of the oscillating plate affect the value of those resonancefrequencies, and what geometric properties of the plate affect the patterns.

8. Let us consider the following circuit: Vin R Vin (a) Find an expression for Vout in terms of Vin, d, R, C, and R. (b) For this part, assume R = R and R*C = 1s. Also take Vin to be a triangle wave of amplitude 1V and period 1s. Draw a plot of Vin and Vout- (The triangle wave should start from zero and rise linearly to its maximum of 1V, which it reaches at t = 0.5s; it should then decrease linearly back to OV, which it reaches at t = 1s.) (c) Consider changing the circuit to: R R Vi-W Cg RE www How would this change your results to (a) and (b)? (Hint: what are in and i, for the op-amp? This isn't hard!) (d) Consider the following circuit: + Find Vout as a function of V₁, R, RF, C, and RE RE ww Rg Ce Vout RE www Vout -Vout