The noun wave is used to denote a wave-like motion produced in a grandstand or stadium by successive sections of the crowd of spectators standing up, raising their arms and sitting down again.

The following, for example, is from a UPI (United Press International) story about the Tigers, a baseball team based in Detroit, Michigan, published in several Canadian and U.S. newspapers on Saturday 12^th May 1984—for example in The Citizen (Ottawa, Ontario, Canada):

Detroit fans, 44,187 of them, gave the Tigers their first look at “The Wave”—a chain-reaction cheer whereby sections stand up and yell consecutively to make it look like a human tidal wave.

This form of wave-like motion through a crowd, which originated in the USA, is said to have been invented by the U.S. professional cheerleader George Henderson (born 1944), a.k.a. ‘Krazy George’.
—Cf., in particular, Who knew? Turns out Colorado was the birthplace of ‘The Wave’, by Joshua Kloke, published in The Hockey News of Saturday 28^th March 2015.

The earliest occurrence that I have found of the noun wave applied to a wave-like motion through a crowd is from a story about ‘Krazy George’, by Gary Taylor, UPI sports writer, published in several U.S. newspapers on Wednesday 16^th December 1981—for example in The Danville News (Danville, Pennsylvania, USA):

Baseball viewers may remember when he had sections of Oakland fans rising to their feet in waves during last fall’s playoffs.

Both the noun wave and the phrase human wave then occur (again in relation to ‘Krazy George’) in the column Viewpoint, by George Watkins, published in the Salinas Californian (Salinas, California, USA) of Friday 27^th May 1983—the author evokes the home games, at the Coliseum, of the Oakland Athletics (the A’s), a baseball team based in Oakland, California:

The biggest thrill for an A’s fan is to become part of the “human wave.” Naturally, Krazy George instigates the “human wave,” which makes it all the more popular.
The “wave” begins early in the game when Krazy George convinces one section to stand up—then another, then another. Soon the entire stadium is standing up and sitting down in sequence—one section alter the other. This goes on for the entire inning (or longer) regardless of what happens on the field. A’s fans think this is the greatest thing they’ve ever seen at a ballpark. Small wonder.
[…]
The A’s also provide another off-field distraction—Diamond Vision—a large movie screen located above the left-centerfield bleachers. It provides instant replays for fans at the park. This allows fans to view the play they just missed because they were too busy being part of the “human wave.”
It’s a credit to the A’s public relations department that they’ve convinced so many people this is the way baseball fans should be entertained.

The following description of the crowd of spectators at the Coliseum, Oakland, California, is from a story about ‘Krazy George’, by Burr Snider, Examiner staff writer, published in the San Francisco Examiner (San Francisco, California, USA) of Sunday 29^th May 1983:

Krazy George is warmed up enough to try his piece de resistance, the famous rolling cheer. Way out at the far end of the left field stands he’s working to teach a whole section how and when to stand up and raise their arms over their heads and cheer like hell. Then he moves down to the next section and explains that as soon as the first section sits down, they will stand up and continue the cheer. Oh, he’s working, George is, it’s not easy getting this stuff across to a couple of thousand rowdy fans, but now everybody’s got the idea, and he’s ready to start the cheer.
The first section stands and cheers, then the next, and the next and the next, and now it’s caught on like a prairie fire, sweeping around home plate and down the first base line. You can watch and hear it thundering toward you like a revolution coming down the street as section after section, all three tiers of seats, wildly obey George’s bidding. Then the wave hits your section, everybody inexorably rises and cheers, and whoosh! it passes on, surging ever and ever faster around the Coliseum. The ballgame itself is forgotten as the crowd becomes mesmerized by this rolling, deafening madness, everybody rising like cilia toward stimulus at George’s command. If it weren’t so much fun it would be hard not to think of Nuremberg and Hitler’s orchestrated rallies. But there on the dugout roof stands George, proudly watching his awesome handiwork, and the goofy grin of accomplishment on his face lets you know in spades that this is the quintessential kid at play here.

This form of wave-like motion through a crowd was popularised worldwide by spectators at the 13^th FIFA World Cup competition, held in Mexico from Saturday 31^st May to Sunday 29^th June 1986.

However, here, the noun wave is apparently a loan translation from the Spanish feminine noun ola. This was mentioned—with xenophobic undertones—by Andy Parker in the column Armchair View, published in the Burton Mail (Burton-upon-Trent, Staffordshire, England) of Friday 6^th June 1986:

It’s not just the ball that behaves strangely in the rarefied Mexican atmosphere.
The thin World Cup air is having its effects on all aspects of the greatest small screen spectacle on Earth.
How confusing, for example, is this new phenomenon, “la ola” (the wave).
The ball may be pinging harmlessly around in midfield, but lack of action won’t stop the excitable Latins from suddenly bursting out in cheers and yells as if bent on bringing the house down.
I was fooled into thinking the first few times this occurred that something interesting might be happening offscreen—but it was only the Mexicans leaping in and out of their seats like so many jumping beans to create the truly wonderful effect of a “human wave’’ going around the stadium.
This is clearly an attempt by the football-viewing public of Central America to compensate for the lack of action in areas where the reasonable-thinking soccer fan might justifiably expect it.

This, in turn, gave rise to the British-English phrase Mexican wave. The earliest occurrence of this phrase that I have found is from the column Square up with Dickie, by the British cricket umpire Harold Dennis ‘Dickie’ Bird (born 1933), published in The Daily Mail (Hull, Yorkshire, England) of Saturday 28^th June 1986:

That Mexican wave caused nasty ripples

YORKSHIRE cricket fans are among the most knowledgeable in the world, and they are also the most faithful!
I often meet them, up and down the country, and usually am impressed by their interest in the finer points of the game.
This is why I was amazed at the behaviour of so many people in the crowd for the Headingley test against India last weekend.
I am, of course, talking about the so-called “Mexican wave,” which seems to have been taken up, after being shown on television during the coverage of the World Cup.
It involves spectators, section by section around the ground, standing up in turn, and raising their arms.
It can look quite effective.
I gather it is supposed to lift the Mexican team, which is fair enough.
But I hope I never see it again on a cricket ground, because it simply is not fair to the batsmen.
I am sure that India’s young star, Mohammed Azharuddin, was put off his stride by the crowd demonstration at Headingley.
For, after the game had been briefly stopped, he was out lbw to John Lever.
Obviously, the paying public were just having a bit of fun and trying to raise England’s morale, as they struggled to get back into the game—but that is not the point.
It is often very difficult for players to keep an eye on the ball when the ground is full, because the spectators provide a multi-coloured and ever-changing background.
[…]
It should not be necessary to tell people not to move about, while the game is in progress, and certainly no one should be leaping up and down as the fans were when doing the “Mexican wave.”