Ok I was going to ask you if it could be a square wave, because looking through my books all RC oscilators have no real frequency change per voltage change.
BUT a multivibrator does.
Heres how I would try it,
Build a multivibrator, then use a variable resistor in one of the base circuits,
then adjust this resistor up and down to see how the freq, changes, once you establish that, then this variable resistor could be substituded with a transistor amp, so then an input to the amp, would cause a change in base voltage at the multivibrator, thereby changing the freq.