The circuit you describe
"electromagnetic relay in series with a varying source voltage source .The relay acts to break and complete the circuit when then the electromagnet is energized"
is a buzzer.
"connect my constant load across the the electromagnet(inductor) of the relay in series with a diode such that the diode conducts when the relay is off"
then the energy released when the contacts break will be absorbed, and the relay wont wear out
(you can get around 1 - 10 million operations normally)
the frequency depends on the pull-in time and the drop out time.
Pull-in time depends on the energy remaining in the coil when the contacts close, ; the resistance and inductance of the relay, and the voltage applied; and the magnetic flux (or stored energy) needed to open the contacts..
drop out time depends on the size of cap used to store the energy released when contacts open, and circuit resistance; and the magnetic flux (or stored energy) at which the contacts will no longer hold open.
"is it right that there will be constant energy stored in the inductor since for low voltage low frequency there is more time to store the energy in inductor and for high voltage high frequency lesser time to store energy in inductor."
roughly, yes but it WONT be exact, because of sticktion in the relay. All I can say is get a decent relay and try it.
What a great experiment! do contact me if I can be more help!