The word "phonetic" has a extra t (phone + ic = phonetic). Etymologically it seems that it is related to ancient Greek morphology and phonology.
Where does this extra t come from?
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The tau (τ) is actually quite expected in adjectives formed from verbs. There is a whole class of verbal adjectives that are based on the suffixes -τέος and -τός. The former expresses the idea of obligation or necessity, whereas the latter expresses the idea of capability (Smyth §2149). For example, if you consider the verb παιδεύω, to teach, then you can form the adjectives παιδευτέος "needing to be taught" and παιδευτός "able to be taught".
The suffix -τικός is in a similar vein. This suffix is also used to create adjectives from verbs, but it expresses the idea of being suited to or related to something (Smyth §858.6d). Thus φωνητικός means "vocal" as φωνέω means "to sound" and the suffix conveys the idea of something related to sound. If you recall one of the other suffixes, -τός, then you won't be surprised to find φωνητός in the dictionary, which means "capable of being spoken" or "utterable".
In conclusion, tau is common in the suffixes of verbal adjectives. It might be helpful to look up a word I mentioned earlier, παιδεύω, to see even more evidence of these suffixes. You can find entries for παιδευτέος, παιδευτός, and παιδευτικός.