The theremin contains two radio-frequency oscillators (or resonant circuits). This is called a "beat frequency oscillator" by physicists and "ring modulation" by some guitarists. One oscillator operates at a fixed frequency, usually about 285 kHz and the other varies between 282 and 285 kHz. When these oscillators are combined, they produce two signals, one at 567-570 kHz and one at 0-3kHz. A diode detector removes the higher frequency so the lower one is left.
The variable oscillator consists of a circuit of capacitors and inductors in which the vertical pitch antenna and the player's hand serve as the a capacitor. The closer the hand is, the greater the capacitance is as capacitance is determined by the distance between the two plates of the capacitor. This is demonstrated by the equation: C=eA/d ,where C is capacitance, e is the permittivity constant, A is the area of the capacitor's plates, and d is the distance between the plates. Moving the hand towards the pitch antenna increases the capacitance of the oscillator's circuit, thereby reducing its frequency, causing a greater difference between it and the fixed oscillatior, creating a higher pitch. The higher pitch is because higher pitches have higher frequencies. When the player's hand is drawn far enough away, the difference between the oscillators is essentially zero, therby causing sound to stop.
The volume is controlled by the fixed oscillator. This oscillator creats a current that causes a high frequency voltage to be carried across its circuit's inductors. These voltages are higher when the oscillator's frquencies are the same (when the hand is away) and become lower when the player's hand introduces more capacitance. This voltage is changed into a DC voltage by a detector. This DC voltage controls a voltage-controlled amplifier. The audio signal from the pitch oscillator is amplified here. Its volume is determined by how much voltage is carried through the volume oscillator's circuit.