The king's new court: Norman Foster is taking on the home of America's national collection

The poet Walt Whitman described the former United States Patent Building – the scene of Abraham Lincoln's inaugural ball – as "the noblest of Washington buildings". So when Norman Foster set about renovating its courtyard – it is now the Smithsonian Institute and houses the American Art Museum and National Portrait Gallery – he was determined to preserve the historical integrity of the building, while bringing the space back to life.

The result is quite a departure in a city as architecturally conservative as Washington DC. As a review of the Robert and Arlene Kogod Courtyard – named for it sponsors – in The New York Times noted; "this city has long been a backwater in terms of contemporary architecture".

But Lord Foster embraced the brief wholeheartedly, proclaiming it a privilege to work "a project with such cultural importance and historical sensitivity to Washington". The design for the courtyard was, he said, driven by a deep respect for the Old Patent Office Building, reinforcing the character of the existing building without competing with it.

Courtyards have become something of a Foster speciality. Most famously, he designed the Great Court at the British Museum, as well as the Treasury courtyard, and he and his team are currently working on a project for the Museum of Fine Art in Boston, where the courtyard is a glass box which sits quite separately from the external wall.

Spencer de Gray, senior partner at Foster + Partners, is keen to emphasise the difference between the new Smithsonian courtyard and the Great Court, while still using the British Museum as a point of reference.

Both were originally built to introduce natural light and fresh air into big buildings, but the Great Court is "all about being a focal point for circulation and facilities like shops, lavatories, cafés and information". At the Smithsonian, however, the loos and information desks are "cloaked within the main fabric of the building", leaving the courtyard as a place to meet friends for a coffee and also a venue for cocktail parties, concerts and speeches.

The most striking aspect of the new $63m (£32m) Kogod courtyard, however, is its canopy roof. Unlike the Great Court, the existing walls at the Smithsonian were not strong enough to bear the load of a ceiling so, instead, the vast, undulating glass roof is supported by eight columns, each clad in aluminium of the palest gold hue, and designed carefully to blend in with the original stonework.

The wave-like structure is an "acoustic" roof, the first of its kind in the world, constructed of deep, diamond shaped panes, into the sides of which is packed recycled cotton from denim jeans to act as sound-cladding, and protected by grilles.

It now acts as a huge acoustic absorber. It is extremely effective because it cuts the reverberation time down to just over three seconds, and that makes conversations very easy, but, more importantly, it's very good for amplified sound if someone is giving a speech, or if there are musical performances in the space.

The roof ripples in response to the central portion of the most historic part of the building, allowing it to skirt around a bay window and pediment, and the rippling idea is continued to encompass smaller bay-windows on either side. There are also good architectural reasons for the design. The more the roof undulates, the more efficient it is structurally; the more like an arch it is.

"It's always good to get one element in a building working really hard for you," says De Gray. At Stansted Airport, another Foster design, it was the bottom, rather than the top, of the building which was exploited, with a huge undercroft dug out to accommodate all the services and baggage-handling, liberating the roof to remain a simple structure that keeps water out and lets natural light in.

De Gray explains: "In the same way, the idea of making the roof here work really hard for its keep solved a lot of problems; the light, heat, the shading, the acoustics. We spent the money in a very wise way, but the structure was doing much more than just keeping the water out."

From the ground, clouds and aircraft can be seen with clarity through the canopy. But closer inspection reveals a milky surface covered in baked enamel-frit dots, which cut out about two thirds of the light, and help to keep the courtyard cool during the baking DC summers. For further cooling, Foster used Roman technology, putting pipes pumping cold water under the dark, stone, floor.

In winter, the water in the pipes is heated, providing a warm surface – it's an energy-efficient method of heating people without wasting energy by heating the whole space. And depending on whether the space is full in summer, or empty in winter, pylons around the edge of the space provide more cooling or heating.

Water is a vital element of the design. When no function is being held in the space, the thinnest skein of water, about a quarter of an inch deep, runs virtually the full length of the courtyard, flowing from left to right and disappearing down a tiny slot in the stone floor. Children delight in splashing around in this wafer-thin river, which can flow at different speeds, thereby altering the clarity of the reflection. But so shallow is the water that just a few steps out of it, feet are dry again.

The very last effect Foster wanted to create was that of a traditional palm-court. So the landscape architect Kathryn Gustafson was drafted in to create as natural a look as possible. In response, she has filled great planters, carved from the same white marble as used in the original building, with olive and fig trees which have been conditioned so that they will neither shed their leaves nor bear fruit.

For when the courtyard is turned over to performances, an acoustician has designed special loudspeakers housed in two of the air supply pylons, and based on speakers from Dutch churches and cathedrals where there is a lot of reverberation. These are very directional and maximise the clarity of the sound.

The lighting is also designed to bring a theatrical air to the space, ranging from simple white light to colours. At night, when the windows of the museum are lit up, the courtyard takes on the character of a town square.

Foster was eager to rekindle the history of the Smithsonian as a social-events building providing a large public living room for people in Washington. Lured in by a family craft-fair, 10,000 people attended the opening of the courtyard over the space of one day, although fire regulations mean it is only intended to hold 1,250 at any one time.

The idea of the urban living room, whether it's totally enclosed, partially enclosed, or completely open, is something that Foster has developed as a theme in our buildings over many years.

Other examples of Foster-designed "urban living rooms" include the Sainsbury Centre at the University of East Anglia, where visitors can view works of art in a relaxed setting, the Sage centre in Gateshead, where the main level is accessible all year round whether a concert is taking place or not, Stansted, and the Great Court.

De Gray says: "This theme of spaces that are not over-specific, not totally prescribed, that are free and accessible, spaces people can go to meet friends, to eat and drink, to relax, as we become increasingly urban in our ways of living, is extremely important in a city."