On 8 February 1974, British United Trawlers lost radio contact with its fishing trawler FV Gaul and 36-man crew. All but two came from Hull. There was no mayday signal, and, for more than 20 years, no wreckage. It left a hole in the city's heart.

The second part of a Hull trilogy, Janet Plater's fictional family drama charts the history of that mystery. Starting the Christmas before the Gaul's departure, it stays with the women and children left behind – their husbands and fathers never found – through a series of inconclusive inquiries.

James Hornsby's Dad, a broad-shouldered belly-laugh of a man, swapped jobs last minute to join the Gaul with his mates. He never returned and, at home, his absence is palpable; his income as well as his person. Mam (Sarah Parks) soldiers on at the kitchen sink. Her teenage son Ian (Niall Costigan), a reluctant trawlerman himself, veers off the rails, while her young daughter Kay (Hester Arden) longs for her dad.

The Gaul's fate hangs over the rest of their lives. The hope they cling to early on, as ships search the North Sea, fades but never fully disappears. There's neither closure nor the cloudburst of grief; nothing to rule out a return. These men – Hull's heroes – hang around like ghosts. They sit behind second marriages. They're glimpsed across town.

Despite dismissive investigations, wary of large pay outs, conspiracy theories swirl around like eddies. Linda (Rachel Dale), another Gaul widow, insists on Russian foul play: that the Gaul was secretly spying. Others refuse to accept human error and, after the wreck's discovery by a television crew 23 years later, Kay attempts to prove a design flaw. When a ship goes down, its swell sucks people down with it. The Gaul ripples all the way to Hull, even now. Patrick Connellan's design has a steel tidal wave hanging over the family home.

Plater's play wears its heart on its sleeve: a hulking historical drama with its nuts and bolts exposed. Exposition and explanation often break to the surface. When they're not talking trawling, characters catch one another up on the day's politics – be it Heath's coalition or Blair's landslide. It can feel clumsy.

Small matter. For the two and a half hours of Mark Babych's staging, the Gaul's seems the only story worth telling. This is theatre that speaks to and for its community; that heals some wounds, and opens others. Over a decade after a reopened inquiry, it ends with unanswered questions. The Gaul retains its mystery. The play demands answers.

It offers some of its own – mostly historical. The Gaul rubs against the tide of nostalgia at play today. It remembers an old way of life fondly, but not flawlessly. Hull's trawlers thrived – "three-day millionaires" back at home – but they risked life and limb to do so. Work bulked them up and wore them out. Plater ties the Gaul's disappearance to the powercuts that followed through three-day weeks; a poignant expression of society's emasculation as industry grinds to a half. Next to that, she sits social change: Bowie bursts out of the radio and materialism flickers into life. The two are inextricably linked by globalisation. The community of old, its left front doors unlocked, has long since broken up. Hull voted for Brexit, 52-48.

It's a play about women: Hull's anchors, Plater calls them, even as she asks how much as changed. By 1997, Kay is a lab assistant, "washing up" after her male colleagues. The Gaul charts media shifts too: from unchecked cover-ups through to the multiplicity of the post-fact internet age. Its potency lies there, I suspect, at a time when we're righting past wrongs, from Hillsborough to Yewtree, the Gaul is another mystery waiting to be put to bed.

The Gaul runs at Hull Truck until 29 October.