The study, conducted by University of Kansas School of Business lecturer and research specialist Midam Kim, asked participants to compare short speech samples of 12 current and former CEOs — including Jeff Bezos, Tim Cook, Mary Barra and Ginni Rometty.
The CEOs' names and companies were not disclosed to the study's nearly 200 male and female participants, which included individuals from both the U.S. and other countries.
Kim manipulated each CEO's sample to create low-, middle- and high-pitched versions. Participants listened to all three pitch levels for each CEO and picked the sample that sounded the most "competent" and had the most "integrity," Kim tells CNBC Make It.
Competence and integrity are both measures of trustworthiness, she notes.
The result: Lower male voices were perceived as more trustworthy, but lower female voices had a much smaller effect on trustworthiness. "For male leaders, the pattern was reconfirmed ... but for female leaders, that pattern was much weaker," Kim says. "People do not care too much about a female CEO having a lower voice."
The study, which has not yet been published in a journal, challenges a common finding across a plethora of older studies that people consistently perceive lower voices as more capable of leading. The reason that it's not really true for women, she says, has to do with differing leadership expectations.
People tend to expect "dominant leadership" from men and "communal leadership" from women, Kim says. In other words, effective male leaders are often associated with characteristics like being assertive, controlling, aggressive and self-confident, while great women leaders are more associated with caring about others and being helpful, kind and sympathetic.
A low voice is an "auditory cue" for dominance, and people don't tend to expect that trait in women since it's not a sign of communal leadership, Kim says.
"If a lower voice, which is a dominant skill, is coming from a female figure, then that is violating people's expectations of female leaders," she adds.
That was especially true for female study participants, who said a low voice helped female CEOs seem more competent but didn't affect their perceived levels of integrity.
Kim also asked the study's participants to rate the CEO voice samples by competence and integrity. Female participants said a low voice helped female CEOs seem more competent, but didn't do anything to make them seem like they had more integrity.
The findings don't necessarily mean a low voice will hurt female leaders, especially if that's your natural pitch, Kim says: You just "might not have to lower your voice intentionally" to sound like a better leader.
Clarification: This story has been updated to reflect that competence and integrity were used as markers of trustworthiness in the study.