What determines radio frequency for a diode? I have a very simple working radio as shown in this schematic:

This radio receives one radio station. 
My question is, what determines the radio frequency that this simple radio is tuned in to?
 A: ANY wires (or conductor) can act as antenna. You have an inductor in the form of the headphones, giving you a natural resonance with a time constant in seconds of L/R. It will still resonate even if it is not amplified, if exposed to em waves around the same wavelength as the time constant. If the EM signal is powerful enough, you wll get audio. 
A: Years ago (1960s) when I worked for the BBC, part of my job was to answer calls from members of the public. One man rang to tell me that he could hear a BBC radio programme from his bed! I asked if he had a metal bedstead, which he did. He lived in Droitwich where the BBC Long Wave transmitting station was situated. [200kHz Light Programme in those days. Later the LW trnsmitter was used to broadcast Radio 4 on a slightly different frequency.] The contacts between different strands of the bedstead would have acted like the coherer of early radio receivers, which predated the quartz "cats whisker" diode and I presume there was enough received energy to make parts of the bedstead matrix vibrate.
