This unnamed officer, played by Madge Sinclair, is the first female Starfleet starship captain portrayed on Star Trek (despite the quizzical TOS: "Turnabout Intruder" reference where Janice Lester believes female captains are an impossibility). In the Pocket Booksnoveladaptation she is referred to as Captain Alexander, but there is no filmed evidence that this was canonically intended to be her name. Several novels, including The Star to Every Wandering, establishes her name as Margaret Alexander and The Star to Every Wandering shows her to have served with Captain Kirk before becoming a captain. She later became married, changing her surname to Sinclair-Alexander and she was promoted to admiral. She was also the officer who recruited Kirk to go on the USS Enterprise-B for the christening ceremony.
This science officer informed the captain that the Whale Probe's call was being carried on an amplification wave that was negatively affecting their systems. He later delivered the damage report, informing her that they were only operating on reserve power, as all systems had failed.