As soon as Katie Hannon starts speaking, you can hear her anguish. “It’s a terrible, terrible day,” she says, by way of opening Wednesday’s Liveline (RTÉ Radio 1, weekdays). The host is of course referring to the murder of 19 schoolchildren and two teachers in Uvalde, Texas. It’s an unspeakable atrocity which she nonetheless has to talk about, sighing deeply while trying to express what she’s feeling. “It’s beyond heartbreaking to look into these little children’s faces and think about what happened,” she says, sounding defeated.

It’s a measure of the horror of events in the US that seasoned radio presenters 6,450km away should be so tangibly distressed, even as a brutal war grinds on in Europe. But as Hannon’s discussion makes clear, revulsion at this latest mass shooting — not long after 10 people were murdered in a Buffalo supermarket in the US — is compounded by the likelihood that nothing will be done to prevent a repeat of the carnage.

The host talks to Galway native John, a school administrator in Texas, who cries after hearing Hannon read out the names of the murdered children. But equally striking is his account of the anti-shooting procedures practised by his students: he describes children being ushered to supposedly secure locations, after which “the kids are locked down in darkness for 45 minutes”. Though occasionally angry at this surreal state of affairs, John just gets on with minding his young charges: “You can’t live your life in fear.”

Such stoicism must be hard to maintain given the apparent impossibility of getting even minimal gun control measures passed by US lawmakers. As an expatriate Chicagoan remarks to Hannon, it’s easier to get a gun than baby formula in the States these days. To non-Americans (and to many Americans as well), an obvious way to help prevent mass shootings is to limit the sale of firearms. But Hannon’s conversation with an American caller — also called John — underscores the political and cultural differences that prevent such measures.

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This John, a gun owner, is appalled by the Uvalde massacre and is “open to a conversation” on restrictions, but doesn’t think such laws work. “This has to stop, but this will not stop through legislation,” he says. “There is no one cause and no one solution.” As befits her journalistic pedigree, Hannon quizzes her guest with quiet thoroughness, but eventually her frustration boils over. “Is there any reason on God’s earth why anyone should need an assault gun?”

It seems a simple question, but after lengthy pondering John cautiously ventures: “I would tend to agree with you.” Even then, he thinks firearms laws are unfeasible as so many Americans view them as a threat to liberty, citing their constitutional right to bear arms. “This country is built on the pursuit of freedom,” he says. “There are dead children,” replies the exasperated Hannon.

It’s only a glimpse of the logjam in the US, but it’s dispiriting enough. Polite and measured, John isn’t a pro-gun fanatic: “I’m just giving you one American’s perspective.” But that such ostensibly moderate voices oppose gun control, even in the face of children being slaughtered, only adds to the sense of despair. “We just live in a state of constant agitation in this country,” John concludes. On this, at least, there’s agreement.

Kevin, an Irish emigrant living in New Jersey, recalls how the US was “revered” in the Ireland of his youth. “That feeling is well gone,” he regretfully observes.

Hannon isn’t alone in being so affected by the Uvalde killings: on the Hard Shoulder (Newstalk, weekdays), Kieran Cuddihy is audibly upset as he talks of mourning parents being robbed not only of their children but also their “imagined futures”. But in bringing Liveline’s ground-level perspective to bear on the subject, Hannon provides vital insight into the uniquely American factors that muddy the moral waters around mass shootings. With regular host Joe Duffy frequently absent of late, she sounds increasingly at home in the slot with each passing week, even when dealing with grim subjects.

Normally, music shows provide a safe haven from sad events. But a melancholy mood pervades Monday’s musical programmes, following the death of Irish singer Cathal Coughlan. Cathal Murray devotes much of Late Date (RTÉ Radio 1, nightly) to songs from the Cork native’s 40-year career as vocalist with the bands Microdisney and Fatima Mansions, as well as his recent collaborative project, Telefís.

“Cathal’s music has been in my life from a very young age,” says Murray, whose impeccably curated selections make his show a consistent pleasure, even if his soothing voice, being so suited to late-night or early-morning slots, must play havoc with his circadian rhythms. Either way, he provides a poignant overview of Coughlan’s uncompromising yet transcendent work.

Coughlan’s death weighs heavily on Tom Dunne (Newstalk, Sunday-Thursday). Normally an infectiously enthusiastic presence — “fantastic” and “sensational” feature heavily in his on-air vocabulary — Dunne is obviously bereft at the news: “I’m rocked on my heels.” But if he occasionally gropes for the words to describe his peer — Dunne’s band Something Happens were signed to the same record label as Microdisney — he conveys why. Coughlan, despite his lack of commercial success, was such a cherished figure to Irish music fans of a certain stripe and vintage. (Including this one.)

Dubbing the late singer as a “genius songwriter”, the host talks of the “raging intelligence” and “withering verbal capacity” that allowed Coughlan to articulate the frustration and anger felt by a generation of young people in 1980s Ireland. “I was slightly afraid of him, I won’t lie. He had that intensity about him,” Dunne says, alluding to his contemporary’s acerbic iconoclasm and brooding stage persona.

It makes for an authentically heartfelt tribute that highlights Dunne’s virtues as a broadcaster, from his amiably unpolished delivery to his emotional openness. (In the past he has spoken about his cardiac operation with bracing candour.) Above all, he shows off his abiding passion for music. Playing one Coughlan classic after another, Dunne highlights what an enormous talent has been lost, and reminds listeners of music’s often bittersweet resonance. Not all loss brings such consolations, as events in Texas attest.

Radio Moment of the Week

Colm Tóibín’s appearance on Today with Claire Byrne (RTÉ Radio 1) is a pure pleasure, with the author displaying his wide-ranging intelligence and impish wit. Tóibín talks about the US’s gun fixation, the nuisance of seagulls and, having published his first book of poetry, the challenges of writing verse: “It really is about inspiration, it’s a kind of miraculous thing.” Having come through treatment for cancer, he sounds energised, but is adamant that zest for life shouldn’t be conditional on surviving such ordeals. “If you need chemo to remind you of how great life is, then there was something wrong with you before,” Tóibín chuckles. Well said.