The way you sound reaches people more directly than what you say. There is a pathway that tunes the ear towards the human voice, and a warm, unhurried voice uses it.

What the research says

The physiology here leans on measures of vagal tone. A methodological review confirms heart rate variability indexes the parasympathetic side of heart control and relates to self-regulation, while stressing how easily the measure is confounded. The particular claim that a warm voice recruits that circuit is anatomically plausible and not something these measures have shown directly. The practical advice costs nothing either way.

Strength of evidence: one line of research. A single study, or a theoretical account.