In the spring of 2014, in one of the most controversial crimes of recent times, Israeli border guards shot dead two Palestinian teenagers in the West Bank town of Beitunia. CNN reporters captured the deaths on camera, disproving the soldiers’ claim that they were quelling a riot; but still the Israeli government defended its own. In the chaotic investigation that followed, audio-ballistic spectrograms of the event produced by the Amman-born artist and “audio investigator” Lawrence Abu Hamdan proved crucial. He was asked – as we are now, in his immensely powerful installation at Nottingham Contemporary – to listen rather than look.

The spectrograms hang before you like targets in a shooting gallery. Each represents a different kind of gunshot, plucked from the soundtrack of carnage; and each approaches or recedes according to the trial unfolding in transcript on a screen below. Were the soldiers firing live ammunition or rubber bullets, as they insisted? Or were they in fact trying to disguise the fatal shots to make them sound like rubber bullets, with murderous intent? Hamdan gave the clinching evidence; but what strikes is the eerie silence of his installation. The case appears more horrifying as the lies and distortions are laid bare on screen, uninflected by the mollifying tones of human voices. The bodies of evidence hang in the air, ghosts of the speechless victims.

Hamdan’s Earshot, recently bought for the nation by Tate Modern and shown in museums all over the world, fills the first gallery in Nottingham and is in many ways the key to the whole exhibition. Everything here is a form of testimony or evidence, a witness to life in the Arab world. Here is a bird’s-eye impression of Cairo after the Egyptian revolution and a photographic sweep through the streets of contemporary Beirut; here is a phone film of a protest in Kurdish Iran and the music of cafe life in Istanbul. One of the largest surveys of Arab art ever mounted in Britain, curated by the museum’s director Sam Thorne, this is a huge coup for Nottingham Contemporary.

This momentous show presents a time and place where art may have become the only place to speak

The show’s title comes, in part, from another profound installation, by the Beirut-based artist and composer Joe Namy, where the viewer sits on a steel bench bathed in purple light before a screen of spooling words, all of them attempts to describe the indescribable. One is the testimony of a translator working on the subtitles to an underground film by the Syrian “emergency cinema” collective Abounaddara, in which anonymous witnesses tell of the brutal execution of a prisoner, his neck slashed from ear to ear. The translator tries to think how to reproduce this phrase without the obvious allusion to smiling, and fails. Since the murder was a hidden horror, there are no images; words therefore matter even more.

For some of these artists, images and words are both equally limiting. The Iranian artist Shirin Yousefi conceals diffusers at sporadic intervals through the show, emitting a spectrum of scents – the spicy perfume of bazaars, the grassiness of upland pastures – that trail an olfactory journey through the Kurdish regions of Turkey, Syria, Iran and Iraq. Malak Helmy fills the museum stairwell with a swelling flood of wild track recorded by a homing pigeon swooping over Egypt from Alexandria to El Alamein. The music of legendary Lebanese singers circles in the air.

Haig Aivazian’s Hastayim Yasiyorum (I Am Sick But I Am Alive), 2016. Photograph: Stuart Whipps

Certain works cannot have quite the same meaning here, perhaps, as they would to viewers in the Arab world. One film records, with stultifying slowness, the evolution of a landfill site outside Beirut and its political significance in the years following the Lebanese civil war. Others centre on family photograph albums, reprised in the form of videos, embroideries or prints, commemorating individual members and their mysterious fate. I could make little sense of Ania Dabrowska’s random archive of found snapshots from Lebanon and beyond, and I’m not sure that the artist has either.

But others return to more traditional means. One of the show’s stars is Haig Aivazian, whose sculptures take the life of a Turkish-Armenian musician and turn it into a resounding metaphor. Aivazian’s beautifully shaped objects have the force of personality in their own right – the long necks of mandolins pulled to the limit on black racks; musical strings stretched to breaking point across the full length of the gallery wall; above all the immensely elongated oud, neckless, its holes like a mouth and two staring eyes, lying on a black case: a body upon its bier. Together, these sculptures form an elegy for a lost culture and its vanished artists; no longer instruments of music so much as torture.

Almost inevitably, this very powerful show must turn upon politics. This can be as light as a calligraphic scroll by the cherished Lebanese poet Etel Adnan, now in her 90s; or as rough as the phone film of the Kurdish artist Hiwa K, who travelled to Europe on foot to escape Iraq in the 1990s. In 2011, Hiwa returned to his hometown, Sulaymaniyah, where he and a pal are filmed playing a haunting Ennio Morricone theme from Once Upon a Time in the West on mouth organ and guitar as they fight their way through a march against the use of teargas. All around them, people keep rallying in the midst of smoke and dust, squeezing lemon juice into their mouths against this very gas, turned upon them once more. This is performance art become living protest.

Forensic Oceanography’s ‘sorrowfully beautiful’ Liquid Traces: The Left-to-Die Boat Case, 2014. Photograph: Stuart Whipps

Which is what marks this show as momentous – its presentation of a time and place where art may have become the only place to speak. This is literally the case with Hamdan, whose testimony proved crucial in life as in art. And it is especially so with a devastating film made by the Forensic Oceanography research group, charting the fate of a migrant boat adrift between Tripoli and Lampedusa for 14 days. The vessel is a twinkling light in a liquid blue swirl on the glowing screen before you. Other lights come and go in brilliant constellations. These are the positions of all the many planes, helicopters, Nato vessels and fishermen’s boats that flicker around the migrants but never draw close. A thousand documents could not say as much as this brief and sorrowfully beautiful film in which all the lights fade, leaving only the one little spark which eventually dies away, emblem of what is now known as the Left-to-Die Boat..

• From Ear to Ear to Eye is at Nottingham Contemporary until 4 March