The final phase of the New Museum’s inaugural exhibition, “Unmonumental,” is largely devoted to work that challenges the traditional definition of what constitutes a museum. “The Sound of Things: Unmonumental Audio” is devoted to sound art and has no visual component, while “Montage: Unmonumental Online” brings together works of Internet-based art, which require no museum at all. The institution has also recently added a more conventional video installation, titled “The Golden Age” (2007), by the Los Angeles-based collective My Barbarian.

Together, this final phase amounts to a remarkably low-key affair. “The Golden Age,” for instance, is almost hidden away in an alcove off a landing along an easily missed internal staircase connecting the third and fourth floors. The alcove itself is small, and perfect for children, whom I understood to be the intended audience of the installation. It plays on two facing video monitors. On one, the three members of the collective, dressed in sailor suits, sing a chipper song about the African slave trade — “They took your baby away, your baby away. Who put the gold in the Golden Age?” — while they do a choreographed dance. On the opposite monitor, a group of people follows along, also singing and dancing.

It’s the sort of thing that, with the addition of colorful backgrounds, would make for fine children’s television. But here the low-budget presentation hovers uneasily between parody and earnestness. Then again, who am I to judge? A child’s opinion would be more appropriate.

A program of short audio collages by 13 artists, “The Sound of Things,” is even more ephemeral. The pieces can be heard throughout the galleries at three-minute intervals, and include chants, whispers, and other noises. When the galleries are relatively empty, the sounds often make for a pleasing supplement to the viewing experience. But when they are more crowded, it’s difficult to distinguish the sound art from the general clatter. And in the galleries, there is no way to tell which artist made which noise — they all blend into a din.

Sound is, of course, all about context; as the old joke goes, the crinkling of a candy wrapper can be music, but the crinkling of a candy wrapper during a Bach performance is noise. What makes the sounds in “The Sound of Things” artistically novel is the context of the museum; people have been making odd sounds since long before the word “art” existed.

By contrast, the Internet remains a truly novel tool, one that has been used for art for little more than a decade. Available at rhizome.org/montage, the pieces by the 14 artists who make up “Montage” demonstrate the range of work that can be created on and for the Web, yet they also point to the imaginative limitations hindering so many who venture into the medium.

Much Internet art consists of cutting and pasting — of sampling the work of others. William Boling’s (b. 1954) “You Ain’t Wrong” (2007) pairs photos that people have placed on the auction sites eBay in America and TradeMe in New Zealand: A pile of metal springs from New Zealand is, for instance, paired with an old photo of a man in a top hat from eBay. Nina Katchadourian (1968) asks viewers to arrange found images of baby animals in order of cuteness in “The Continuum of Cute” (2007–08). And for his project “50 50” (2007), Oliver Laric (b. 1981) has spliced together 50 amateur performances of songs by rapper 50 Cent, all ripped from YouTube.com. Needless to say, it’s considerably funnier and more engaging than Mr. Boling’s forced couplings.

One would imagine that any use of an artist’s own product would only improve on the arts-and-crafts level of achievement. But Charles Broskoski (b. 1982) would prove this assumption wrong. His “Cube” (2007), a grid-like image made of Mac OS X scrollbars, creating the illusion of a 3-D box, comes off as a schoolroom doodle for the high-tech age, but with less energy than such a description suggests. And in online art it is energy — intellectual energy, imaginative energy — not the medium that seems to be the problem.

For a counterexample, consider Jessica Ciocci, a member of the talented collective Paper Rad, who brings considerable intellectual and imaginative juice to her project “instient.mash” (2007). Exploiting the seeming limitlessness of Internet “space,” Ms. Ciocci’s virtual collage pastes together photographs, drawings, digitally produced imagery (stripes, a flickering pot leaf), writing, and other images to produce a hyper-colorful tableau. Far larger than your desktop, the collage allows you to scroll through it and, at points, go in deeper; you can, for instance, click through to an excerpt of a novel mistakenly sent to the artist by Amazon.com.

Still, the most impressive piece here belongs to the Chinese artist Cao Fei (1978). “Chinatracy” (2007) gets its name from Ms. Fei’s Second Life avatar, China Tracy, who is the protagonist of a three-part, 28-minute-long documentary “filmed” entirely in Second Life. It is a beautifully rendered poetic meditation on, in part, how the utopian dreams and fantasies with which people imbue this virtual otherworld are inevitably infected by our real-world hopes and foibles — “for sale” signs recur here, for example. The music, by Prague, is lovely, and many of the words spoken come from an Octavio Paz poem.

Cao Fei shows that the online collage aesthetic can be driven by a powerful imagination; it doesn’t always have to be about rearranging dull blocks in an inherited framework.

But all the work in this last phase of “Unmonumental” has an aptly experimental feel. And, as in all experiments, gains can be made from the failures as well as the successes.

Until March 30 (235 Bowery at Prince Street, 212-219-1222).