Ok i understand what you mean now. Here is basically how an LC oscilatior works. (to give you an understanding of how each component works within the circuit.)
Suppose a capacitor is charged by a battery. Once the capacitor is charged, one plate of the capacitor has more electrons than the other plate, thus it is charged. Now, when it is discharged through a wire, the electrons return to the postive plate, thus making the capacitor's plates neutral, or discharged. However, this action works differently when you discharge a capacitor through a coil. When current is applied through a coil, a magnetic field is generated around the coil. This magnetic field generates a voltage across the coil that opposes the direction of electron flow. Because of this, the capacitor does not discharge right away. The smaller the coil, the faster the capacitor discharges. Now the interesting part happens. Once the capacitor is fully discharged through the coil, the magnetic field starts to collapse around the coil. The voltage induced from the collapsing magnetic field recharges the capacitor oppositely. Then the capacitor begins to discharge through the coil again, generating a magnetic field. This process continues until the capacitor is completely discharged due to resistance.
Technically this basic LC circuit generates a sine wave that loses voltage in every cycle. To overcome this, additional voltage is applied to keep the oscillator from losing voltage. However, to keep this oscillator going well, a switching method is used. A vacuum tube (or a solid-state equivalent such as a FET) is used to keep this LC circuit oscillating. The advantage of using a vacuum tube is that they can oscillate at specified frequencies such as a thousand cycles per second.
Unfortunatly i do not have any circuit design software on this computer so i can not hook one up for you. However i believe your circuit will work however you must pay very close attention to component values in order to get the right frequencies you require. also you may wish to hook up a low pass filter that attenuates any frequencies above 500 Hz. this should be connected as in this link -
http://image.absoluteastronomy.com/...ages/1/1s/1st_order_lowpass_filter_rc.svg.png
with the resistor being - 10ohms and the cap being - 30uF.
Also you may wish to amplify the signal before you output it to the Speaker. as before i have no design software with me atm however get back to me when u have hooked this up and i will send u all i have on op amps to help you along.
Hope this helps,
Good luck!!