There was the sound of Donald Trump leaving the White House for the final time, clattering over the city in Marine One, his helicopter taking a circuitous, look-at-the-sights-as-we-leave route. There was the sound of his final boasts, as he spoke at Joint Base Andrews about his administration’s purported accomplishments.

There was the richness of music and melody, of Lady Gaga and Jennifer Lopez performing on a day like no other. There were the notes of both optimism and clear-eyed reality in the poetry of Amanda Gorman, the 22-year-old strikingly honest about the nation’s inequality, yet suggesting “there is always light, only if we are brave enough to see it”.

Then there was the gruff familiarity of Joe Biden, solemn and serious, still taking in the occasion and everything that had carried him to this moment, as he was sworn in as the US’s 46th president by Chief Justice John Roberts, noting that to “secure the future, America requires so much more than words, it requires the most elusive all things in a democracy: unity”.

Yet, if there was one sound most frequently heard on Wednesday as Mr Biden took the oath of office at the age of 78, it was that of a sigh of relief.

For supporters of Mr Trump, now the former president and with an uncertain future, there was no doubt regret and indignation. Almost 75 million Americans voted for the Republican candidate, and a large portion of them believe falsely that the election was stolen from them.

For many more, however, there was a sense of pleasure that Mr Trump’s term had come to an end and that Mr Biden and Kamala Harris had taken office. The fact that the inauguration – protected by thousands of troops – had gone off smoothly following the attack on the Capitol just two weeks ago, was in itself cause for celebration. It also spoke to just how anxious and weary many people feel.

“I’m so happy that this is happening,” said Reva Gupta, 54, who was born and grew up in DC, but whose family had come to the US from Rajasthan in India. “When they won, my mother called me in tears. She was so excited that a woman of colour, a black woman, could be in the second highest office.”

She added: “But they face so many challenges – fairer immigration, the environment, the pandemic. We have to move forward.”

The US holds a presidential election every four years. Many presidents, such as George W Bush, who pushed America to invade Iraq and engage in the war on terror, have proven to be hugely divisive.

Mr Trump, who was elected as an anti-establishment outsider poised to “drain the swamp”, perhaps stands alone for dividing opinion. To his supporters, he is the one man who speaks the truth.

Yet to his critics, he is someone who singularly undermined so much of what people had worked for in the years that preceded him, who stirred up racial hate, stripped away environmental safeguards and bullied those who did not give him what he wanted. 

The United States may not be the beacon of perfect democracy it seeks to suggest to the world that it is.

Yet while people such as Stacey Abrams and Bernie Sanders have sought to counter inequality by expanding the vote and boosting democracy, Mr Trump and the Republicans sought to suppress the vote and cut off access to the tools of change.

In the past few weeks, he and his lawyers had been scrambling in the very bowels of the electoral college system, desperately searching for a weak spot for leverage, whether it was inviting “electors” to DC to meet him at the White House, or calling the Republican election chief in Georgia, and demanding he “find 11,780 votes”.

“I am delighted he has gone. Trump has never cared about the working people,” said Martha Luca Duque, 54, who had travelled from Florida to watch the spectacle.

Most Americans know that the departure of Mr Trump will not suddenly solve the problems. The pandemic has already left 400,000 dead, and wrecked the lives of many.

Yet there is a certain symmetry about what happened on Wednesday, and what played out four years ago when Mr Trump was inaugurated and spoke of ending the nation’s “carnage”. 

In truth, the economy he inherited from Barack Obama was booming, so strong he almost rode it to reelection, and might have, had the pandemic not struck and he failed to adequately respond.

This time, the carnage was real. Who knows how many more will have lost their lives to the pandemic by the time everyone gets the vaccine? This time, Mr Biden felt the situation so pressing that he asked the nation to pause in silence to honour those who had lost their lives – the silence itself another sound that marked the city.

“As my first act as president I’d like to ask you to join me in a moment of silent prayer, remember all of those who we lost this past year to a pandemic,” he said. “Those 400,000 fellow Americans – mums, dads husbands, wives, sons, daughters, friends, neighbours and co-workers. We will honour them by becoming the people and the nation we know we can, and should be.”

Usually on Inauguration Day, the city is packed to the rafters, mostly with people from the winning party, but also those who want to be part of history, and who bring their children and relatives.

This year, officials had told people to stay away. Many had been scared off by the threat of more violence from the extremists and white supremacists who were among the Trump supporters who stormed the Capitol two weeks ago as legislators were voting to affirm Mr Biden’s win.

So while this year there were far fewer people, their determination to be here made them stand out.

Melissa and Thalia, who gave only their first names, came all the way from California for the ceremony. They bought their plane tickets back in November, just after the election. They were not put off by the event being closed to the public. 

Instead, they huddled together and watched on their phone from Black Lives Matter Plaza, just behind the White House. 

“The last four years were very scary to be honest. You have to be careful what you do and how you act. Now it’s nice to be able to breathe,” said Thalia.   

Melissa added: “We’re Mexican-American, and female and gay. So it was scary times. Now it’s kind of a relief.”

Alan Unkle came from Cedar Rapids, Iowa, with his wife.  

“To me it’s a hope for change, finally. To finally wake up from a nightmare,” he said. “It’s been crazy. It’s sad that as a minority to wake up one day and see that the president posted a video with guys chanting white power, not knowing where you stand in your own country anymore.”

He added: “The sad thing is, I just want to see normalcy.”

Even during a non-pandemic year, most Americans, along with the rest of the world, view events on television.

Anyone tuning in this year would have seen a slightly stripped down ceremony, taking place with an air of defiance. 

There were also many trappings of other inaugurations – the past presidents and their wives, the laying of a hand on the Bible, the swearing of the oath of office, the promise to be a president for everyone. Donald Trump was not present, but his deputy, Mike Pence, was.

When the Democrats started the process of seeking to find a candidate to challenge Mr Trump, Mr Biden was the first choice of very few. He was seen as too old, too middle of the road, too much part of the establishment, the supporter of too many foreign wars.

Yet as his campaign picked itself up after several early defeats and he gathered traction, he took on the mantle as the imperfect but “good enough” candidate.

When he spoke on Wednesday, Kamala Harris close to him on the stage, he appeared to understand not only that, but how difficult their work will be.

He also reflected that just weeks ago, rioters had occupied the steps he was now standing on, and that despite that democracy had prevailed.

“Few people in our nation’s history have been more challenged or found a time more challenging or difficult than the time we’re in now,” he said.

Then the “good enough” candidate promised to give it his all as the nation’s new president.

“On this January day, my whole soul is in this: bringing America together, uniting our people, uniting our nation,” he said. “And I ask every American to join me in this cause.”

Additional reporting by Richard Hall in Washington DC