I'm gonna show you How to make a Simple FM Transmitter that works with only an AA battery.
47 pF Ceramic Capacitor x1
33 pF Ceramic Capacitor x1
10 pF Ceramic Capacitor x1
22 uF Electrolytic Capacitor x1
2SC655 (or BC548) Transistor x1
Single Battery Holder (AA Size)
10cm Magnet wire x2
Audio Signal Source (e.g. a MP3 Player)
Step 3: Make the Coils
Do the same for the second Magnet Wire, too.
...Then Solder them on PCB
Step 5: Turn on your Radio
Connect the "Audio In" of the Transmitter to your MP3 Player (or any other non-amplified things playing music).
Place the Battery in the holder.