A crystal radio uses a tuning circuit made of a fixed-value capacitor and a sole

Question

A crystal radio uses a tuning circuit made of a fixed-value capacitor and a solenoid whose inductance can be varied by sliding a contact along the outside of the cylinder (changing the length of the solenoid). The solenoid is made out of a tube wound with wire at a turn density of 35 turns/cm. The sliding contact is initially the middle of the solenoid where the radio picks up a station broadcasting at 520Hertz. Moving the slider by 3cm tunes the station to 1040Hertz.

a)To get the higher frequency, was the solneoid shortened or lengthed?
b)What is the cross sectional area of the solenoid? Hint: Work out a general relationship for the resonant frequency of the RLC circuit in terms of the fractional length of the solenoid.
c) what is the value of the capacitor
d) Describe why its better to use a handle thats 2.5cm in diameter compared to the cylinderical handle of 12.7cm in diameter as a form to wind the solenoid

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