I may be misunderstanding the question, but in the case of an automated phone interface, these are likely just touch tones issued by the computer to redirect your call based on your responses. if you were to respond by pressing a key, that same tone would be issued by you instead. the touch tone interface replaced the rotary interface (using a number of timed pulses) with audible tones for the standard 12-button phone interface.
if you are talking about a clicking noise that sounds like typing on a keyboard, then it may be what the other answers are indicating as aesthetic noise.
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