What are the sources of variability in vowel production?

The acoustic realisations of phonoligical vowels vary for a large number of reasons. We shouldn't expect the signal we pick up from the microphone to be identical for every vowel in every environment on every occasion by every speaker.

One way to classify types of variability is to consider the speech chain story of vowel production:

1. Phonological. The phonological specification of the vowel can change from speaker to speaker: particularly if they have different accents. Speakers of a General American accent have a different set of open back vowels to RP speakers. The distribution of segments across lexical items can vary too, for example for Southern and Northern pronunciations of "bath".
2. Phonetic. The realisation of the phonological vowel by the articulators will depend on the phonetic context: what adjacent articulations need to be made; on the position of the segment in the prosodic structure: what duration and pitch are required; and on the particular gestural preferences of the speaker.
3. Acoustic-Phonetic. The filtering of the sound source generated by the larynx depends on the configuration and size of the vocal tract. Adults and children have different size tracts as well as different size larynxes. Larger cavities lead to lower formant frequencies. Larger larynxes lead to lower fundamental frequencies.
4. Acoustics. Between the sound being generated and the sound being picked up by the microphone, the sound can be altered by background noise and by other "channel" effects such as reverberation, or telephone line distortion. Also note that speakers can change their style of speaking in noisy surroundings.

Finally, remember that the articulators are not precise mechanical devices and you should expect random variation from repetition to repetition.