In a small study (subscription required), researchers at Northwestern University analyzed the subcortical auditory regions of bilingual and English-speaking teens by recording participants' brainstem responses as they heard speech sounds in silent and noisy settings. The Atlantic reports that results showed:
The monolingual and bilingual subjects responded similarly in the quiet condition. Against a backdrop of background noise, however, the bilingual brains were better at encoding the fundamental frequency of speech sounds known to underlie pitch perception and grouping of auditory objects, indicating improvements in auditory attention and working memory.
[Researchers concluded] bilingualism yields functional and structural changes in cortical regions of the brain dedicated to language processing and executive function.