The shocking tirade happened on a train between Haymarket and Edinburgh Park, around 1.30pm on March 1.
The suspect was described as white, around 5ft 8, aged in his late 30s, of a heavy build and with short dark brown hair.
He was wearing a red polo shirt, a black jacket with white piping around the cuffs and blue jeans, and spoke with a Scottish accent.
Officers from British Transport Police said the suspect is thought to have alighted the train at Stirling.
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