Hope this has not already been said, but the resonant frequency of a circuit, parallel and series, is given by the formula, f0= 1/(2* Pi * root[L *C])...........(F1)
Where:
f0 = frequency in Hertz
Pi= 3.142
L = inductance in Henrys
C = capacitance in Farads
To answer your question about different values of L and C producing the same resonant frequency, that is true- they will all have the same resonant frequency but the impedances of the circuits will differ; in general, the lower the L and the greater the C values, the lower the impedances of the resonant circuit.
The reactance of an inductor is given by the formula XL= 2 * Pi * f * L .........(F2)
Where:
XL = inductive reactance in Ohms
f = frequency in Hertz
Pi = 3.142
L = inductance in Henrys
The reactance of a capacitor is given by the formula XC= 1/(2 * Pi * f * C) .......(F3)
Where:
XC = capacitive reactance in Ohms
f = frequency in Hertz
Pi = 3.142
C = capacitance in Farads
Notice that the formulas for XL and XC are reciprocals so that when the inductive reactance and capactive reactance are the same they cancel each other out in a series tuned circuit and add to each other in a parallel tuned circuit; this is the essence of resonance. This is a simple explanation which omits the finer points, but if you had perfect inductors and capacitors the impedance of a series tuned circuit would be zero Ohms and the impedance of a parallel tuned circuit would be infinity Ohms.
A Xtal radio set is all about power transfer. You need to extract the maximum power from the antenna and feed that into the detector diode (Xtal) and then you need to get the maximum power into the headphone from the detector. To get maximum power transfer the power source and power sink should have the same impedance. This is known as the maximum power transfer theorem (don't confuse this with matching most transistor audio power amplifiers, bench power supplies, or batteries to a load which is a completely different matter).
The only problem is that the more you load a resonant circuit, the more you lower the Q, so the design of a Xtal radio is a balancing act.
There is quite a bit about Xtal radios and detectors on the 'Transistor Equivalent' thread:
https://www.electro-tech-online.com/threads/transistor-equivalent.146091/
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