Answer Happy

140 points) A Theremin is a musical instrument invented in 1928 by Leon Theremin, who was interested in translating human movement into music. While not common, the instrument has become something of a cult phenomenon, primarily finding use in horror movie soundtracks and more limited use in popular music. Milhouse serenaded Lisa Simpson with one on a recent episode of *The Simpsons". The Cleveland Science center has one that you can play with. To play a theremin, the artist moves their hands around two antennas (without touching them): one hand controls the volume and the other controls the pitch. Each circuit (volume and pitch) contains a variable capacitor-the human body is is one "plate' of a capacitor, and moving your hand around each antenna changes the capacitance. Let's S see how this works in detail by analyzing the pitch oscillator circuit the output tone is generated by subtracting the resonant frequency of a variable LC circuit from a reference LC circuit operating at 173.4 kHz. OVO L = 598 H C = 55.5 nF C = variable subtract frer 173.4kHz fvar = ? four = frer - far

1) Consider the variable capacitor. What is the resonant frequency (f) when your hand is very far from the antenna? What is the output frequency? Does that make sense? 2) When your hand is very close to the antenna, f 171.6 kHz. What is the value of the variable capacitor? What is the frequency of the output? Does that make sense? 3) The whole audio frequency range is covered by moving your hand from close to the antenna (say, 1 cm) to very far away (say, 1m). How accurately and steadily) does the player need to hold their hand (in mm) in order to sound a specific frequency (say within +/- 1 Hz)