A oscilloscope would be useful in analyzing the waveforms produced by this circuit, but it is not essential. An audio detector is a very useful piece of test equipment for this experiment, especially if you don't have an oscilloscope.
http://www.allaboutcircuits.com/vol_6/chpt_6/7.html
Here is a phase-shift audio oscillator with excellent distortion characteristics thanks to softened diode limiting provided by the 1N914 and resistor divider and degenerated gain provided by the 68 ohm emitter resistor.
http://www.techlib.com/electronics/audiooscillators.htm
As a piece of test equipment, an audio oscillator has to be considered essential for anyone working in with hi-fi gear. Together with an audio millivoltmeter, and even better if you have access to an oscilloscope, you will be able to make proper measurements on everything from preamps, RIAA equalisation stages, tone controls, crossover networks,etc.
http://sound.westhost.com/project22.htm
The circuit is a fairly easy design: It consists of the actual VCO (ICL8038 with supplement parts), the sine and triangle output stage (LT1210) and the CMOS-compatible output stage using the MOSFET driver chip ICL7667.
http://www.triplespark.net/elec/oscillator/ICL8038/
To speed testing, the circuit generates a composite audio signal comprising 10 sine waves of 10 different equal-amplitude frequencies across the audio band. Values stored in EPROM determine the frequencies.
http://www.edn.com/archives/1994/070794/14DI7.htm
Two oscillators, one adjusted to 7.02 MHz, the other to 7.20 MHz, together form a stereo sound carrier generator for 13 cm ATV Tx. Both oscillators are built identical and the outputs are simply put in parallel.
http://pe2er.nl/13cmATV/index.htm
http://margo.student.utwente.nl/el/analog/audosc.gif