WW, both fetal memory and fetal hearing and responses have been studied. The latter especially has been rather well documented. And yes, a baby does respond to similar speech/ speech prosody patterns (songs/rhymes/lullabies/stories)that the mother has familiarised it with when it was in the prenatal period.

Reminds me of an Indian mythological tale that I read years ago, from the Mahabharata or the Panchatantra. (The former is one of the great INdian epics, the latter is from around the same period, but is a collection of stories usually with a moral ending, and contributed many tales to the Arabian nights). It is the story of Ashtavakra. His father was the greatest Vedic scholar of the time. When pregnant with him, his mother, desirous that the as yet unborn child should be exposed to the great Vedas as much as he could, decided to spend more time everyday, in the room where the Vedas were recited . The child started learning at a rapid rate. One day, a group of scholars arrived at Ashtavakra's home to clarify some doubts that they had with the Rig Veda. In the midst of their scholarly debate, the child (foetus actually) interrupted the father and corrected his take on the very point. (Ok! It is a myth!..but a telling one)So great had his learning in the womb been that he had picked up nuances that had skipped the father's knowledge even. The father was humiliated and enraged and his ego was bruised enough for him to curse his son that he would be born deformed in eight places in his body(Ashta-eight; vakra-crooked). Poor Ashtavakra. He had not as yet learnt to not speak out of turn! The father repented immedaitely, but a curse is a curse and it cannot be withdrawn. He therefore added a rider saying that the day Ashtavakra would defeat a gathering of the greatest scholars of the land in Vedic debate, in the King's Court, his bodily deformities would be cured. Which Ashtavakra did at the age of eight(?) and was cured and all was well that ended well......
Point of the story, you ask?........Learning in the womb and do not speak out of turn especially in the midst of elders

In India, all pregnant women are mandated almost to experience good emotions, culture, music, diet, intellectually stimulating exercises and every effort is made to keep them in cheer and happiness, so that the baby is born in a state of good mental and physical health. To this end, there are special functions for almost every one of the nine months and each one is celebrated with much pomp and gaiety especially the one in the eighth month, the bangle festival (my translation). Everyone invited gives the mother-to-be a set of new bangles and gifts and individual wishes welcoming the baby are whispered into the mother's ear.
Have I been on a roll or what......????