In your circuit board, there is a microprocessor running code that takes the measured voltage, Vout(*), and converts it to a frequency, fout (>). The conversion is linear, which means that the frequency and voltage have the following relationship: fout (~) = a Vout (») + B, where a and B are constants. Specifically, voltages gond = 0 V and Vmax = 3.3V will be converted to frequencies of från = 100 Hz and fmax = 2 kHz, respectively Interestingly, humans hear notes exponentially in frequency! Every octave (series of notes that begin and end with the same note) approximately doubles in frequency. For instance, middle C{called C4) has a frequency of 261.6 Hz, C5 (the next octave up) has a frequency of 523.3 Hz, and C6 (the next octave up) has a frequency of 1046.5 Hz Each octave is divided into 12 steps, called half-tones. These are the actual notes of a musical scale. The half-tones of a keyboard increase exponentially in frequency in the following way: f(n) = 2(R-3)/12 X 440 Hz where n is the index of the key on the keyboard (the 49th key is A4, which has a frequency of 440 Hz). Expand this box to see a table of frequencies along the keyboard Scale Show Keyboard Scale - part a 0.0/1.0 point (graded) (Part a) Now think back to the voltage divider of length L, out of which we want to make a resistor piano using a frequency that is linear in the voltage. If the frequency range of the resistor piano spans two full octaves, such that f(* = 0) = fo, then f(x = L) = 4fo. Convince yourself that this makes sense, since the frequency doubles with every octave. If we wanted the first octave to occur at the exact MIDPOINT of the resistor piano, how should the resistance of the paper from » = 0 to » = 1/2 compare to the total resistance of the paper? In other words, determine R(L/2)/R(L). R(L/2)/R(L) = Save Submit You have used of 5 attempts Keyboard Scale - part b 0.0/1.0 point (graded) (Part o) For the case above, how does the width of the paper in the region between x = 0 to * = L/2 compare to the width of the paper in the region » - L/2 to * = L? a) the width of the paper in the region 2 = O to = L/2 is larger
b) the width of the paper in the region > = O to % = L/2 is smaller
c) the width remains constant