Question

On average it takes a person about how long to pick up on your attitude from listening to the tone of your voice?

Answer 1

Ten seconds for words, 0.1 second for sounds.

Explanation:

The last reference contains many additional sources of published research on this topic, but not primarily with a time-based focus. Specific values are really approximations, at best.

10 seconds
http://www.dummies.com/careers/business-communication/communication-business-skills/improving-your-inflection-on-the-phone/

It takes the brain just one-tenth of a second to begin detecting human emotions from a vocal sound, faster than detecting it from their tone of voice, regardless of whether it was a positive or negative emotion being conveyed.
https://www.relationshipscoach.co.uk/blog/brain-detects-emotions-faster-from-human-sounds-than-words-or-tone-of-voice/

Primary Research references:
https://www.mcgill.ca/pell_lab/files/pell_lab/pell_biolpsychology_2015_0.pdf