The Physics of the Wave

What a lovely day at the ballpark! The weather is perfect, our team is showing some signs of life with a four-game winning streak, and – most importantly – we all got our bobbleheads. After we put up a three-spot in the second inning, the mood was so giddy that we couldn’t help ourselves. The wave began rolling around the stands.

There are many conflicting stories as to the origin of the wave. However, I like to think I was there at its birth. In the early 1980s I was in graduate school at Cal Berkeley.  I frequently took Sundays off with a few other renegade physics geeks to go see the Oakland Athletics.

At nearly every game, an uber-fan known as Krazy George did an unprecedented job of engaging the crowd. He had greater skill than an orchestra conductor. Using only his hand-held drum, a booming-but-hoarse voice and unlimited energy, he directed us in one stunt after another.

Sometimes it was just rhythmic clapping. At other times, he coordinated dueling chants between the first- and third-base stands. His pièce de résistance was what has come to be known as the wave. Over time, the wave has become so popular that even celebrities must participate.

The physics of the wave is pretty easy to understand. The fans in one section stand up, raise their hands, shout, and sit back down. Then the fans in the neighboring section do the same, causing the wave to roll around the park. So, while the wave moves throughout the stands, the fans never roam from their seats.

The people move up and down perpendicular to the motion of the wave itself.  Physicists call this a “transverse wave.”  If you think I’m the only nerd to find the wave through the stands intriguing, here is a scientific paper on the topic.

A transverse wave is exactly the kind of wave pulse you can imagine running down a string. Okay, you don’t have to imagine it. Go grab a piece of kite string and a friend to hold one end. You hold the other end without pulling the string too tight. Now, gently pluck the string and – viola – you have created a transverse wave. Individual pieces of the string move back and forth ( or up and down). Meanwhile, the wave itself travels along the string perpendicular to the motion of the individual pieces of the string.

Transverse waves are exactly the kind of waves you create when you strum your guitar. More to the point, transverse waves are created in a baseball bat by its collision with the ball. That’s right, the ball plucks the bat in the same way your finger plucks a guitar string.

I know you’ve felt that “hand full of bumble bees” when you hit the ball off the end of the bat. The pain is caused by transverse waves in the bat initiated by the collision with the ball. Don’t believe me? Check out this YouTube video produced by the Discovery Channel show, Time Warp.

At 10,000 frames per second, you can see many remarkable features of the ball-bat collision. For now, focus on the transverse wave that’s created in the bat from the collision. The wave travels up the bat from barrel to handle while individual pieces of the bat just move back and forth perpendicular to the wave.

It is these transverse waves that explain broken bats. You know that ocean waves grow in size as they go from deep water to shallow water, eventually crashing near the shore. Similarly, the waves starting in the thick barrel of the bat grow as they move toward the thinner parts of the handle.

If the wave in the handle gets too big – snap! – the bat breaks. You may have wondered why the bat always breaks at the handle even when the ball hits the end of the barrel. Now you see it is the transverse wave traveling up the bat that actually causes the break.

You don’t have to rely on video from a laboratory. You may have seen actual game footage of the ball-bat collision presented by Fox Sports during its playoff coverage. Some teams also use a high-speed camera for their regular-season games, such as the Rockies and Yankees. Additional in-game images can be found on Alan Nathan’s Physics of Baseball website or at MajorLeaguePhysics.org.

Transverse waves in the bat produce other effects besides sore hands and broken bats. It takes energy to create these waves in a solid wood bat. Guess where this energy comes from? That’s right. It comes from the energy available to propel the ball.

So, a well-hit ball will induce smaller waves in the bat than a poorly hit ball. Now we are close to understanding the so called “sweet spot” of the bat. Have you ever noticed that if you pluck a guitar string near the middle, it is louder than when you pluck it very close to an end? Where you pluck a string has a lot to say about the size of the waves you create.

The waves on a bat are a bit different from a guitar string. Since the ends of the string are tied down, plucking the string in the middle gives the loudest sound. However, the ends of a bat are free to oscillate, so it turns out that the biggest waves occur when the end of the bat is plucked by the ball.

There is a place in the middle of the barrel where the ball will create the smallest possible waves. When the ball strikes at this location, the least amount of energy will be lost to the waves in the bat. This spot is a “sweet spot,” and most well-hit balls leave from this part of the bat.

Hey, our leadoff hitter just hit a duck snort out to right. I can see him standing at first base wringing his hands, trying to get the sting out of them. I guess he got the opportunity to study transverse waves personally. Anyway, gotta go – here comes the wave again.