The white Apple iPhone or iPod-style headphones were looped around the back of the sock.
Alan Jeal was discovered on Perranporth beach in Cornwall three months ago with injuries to his head, chest and hand.
A post-mortem examination found the 64-year-old from Wadebridge had also suffered extensive internal injuries.
Officers, who are treating the death as "suspicious", believe he was in Truro city centre on the evening of February 24, the night before he was found dead.
Devon and Cornwall Police say there are signs he may have drowned, but this has not been confirmed as the cause of death.
Items of clothing, Mr Jeal's bank card, a credit card, a Nokia 1110i mobile phone and a third generation iPod shuffle are still missing.
It is thought Mr Jeal, who lived alone and was not reported missing, took the number 594 bus from Wadebridge to Truro, arriving in the bus station at 6.14pm.
He is then believed to have got a bus from the Lemon Quay in Truro to Perranporth at around 6.50pm.
"We believe he may have had a friend in Plymouth and another in Redruth, and would like to speak to them as they may be able to provide crucial information and fill in some of the gaps.
"During the investigation we have discovered that Alan was into online gaming and detectives would also like to hear from anyone who interacted with him online."
Mr Jeal's sister, Linda Danielis, said she was desperate to know how her brother had died and appealed for help from the public.
"More than anything I want answers, realising that there is nothing I can do to bring him back," she said.
Anyone with any information that could help the investigation is asked to contact police on 101 or Crimestoppers, anonymously, on 0800 555111, quoting reference 381 of 1 March.
Skynews

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