The Great tenor Enrico Caruso broke a glass goblet by singing a note, and Tacoma Narrows Bridge collapsed in Nov. 7th 1940 due to gusty winds, how did these events happen, and what do these events have to do with baseball?

Both of these events explains two phenomena in baseball: the stinging and the breaking of the bat.

Lets first look at another object: a spring. When you push down a spring and let it go, it oscillates moving back and forth for some time. If there wasn't another other external forces such as air and gravity, the spring would oscillate forever. So if you exert a force on a spring, it will oscillate. This is the same for bats. If you put enough force onto the bat, it will oscillate and it is this oscillation that makes the bat sting or break. But you might ask, why doesn't the bat sting or break every time the ball hits the bat? Read on to find out why.

Lets examine what happened in the with the goblet and the bridge first. Although you may see objects such as concrete, glass, and wood as inelastic materials (you don't see them vibrating when you hit them, do you?), they are indeed, in general, elastic like rubber, though not as much. Every object has a natural frequency or resonant frequency. The resonant frequency is the frequency applied through external force which will generate the maximum amplitude. What is an amplitude? Amplitude can be thought as the size of a wave.

Wave 1 = Blue
Wave 2 = Yellow

According to physics, energy transferred through wave is proportional to square of the amplitude. So what happened when Enrico Caruso sang was that the pitch of his voice matched the resonant frequency of the glass goblet, forcing the goblet to oscillate at its maximum amplitude. So the maximum energy would have been transferred, thus breaking the goblet. It is the same case with the Tacoma Narrows Bridge. The wind swung the bridge at the resonant frequency thus snapping the bridge in half. It might be interesting to note that some marching soldiers break step while crossing a bridge to avoid matching its resonant frequency. So, how does this apply to bats?

As you might have guessed by now, bats also have a resonant frequency. While bats are certainly hard objects, they are not "stiff" objects. When hit by a ball, a bat will vibrate, though you will not feel it every time. The amount of vibration you feel is dependent on the amount of oscillation. So what determine the oscillation?

Since the bat is not a totally symmetric object, the place where the ball hits the bat determines the frequency and the amplitude. Two waves will be generated as the ball hits the bat: the initial wave when ball hits the bat and secondary wave as the ball leaves the bat. Waves would look something like the diagram above. The places where the two waves meet are called nodes . In physics, those nodes are called points of destructive interference. The places were the waves are furthest apart are the antinode or constructive interference. If the ball hits the bat at its antinode, the bat will sting or even break. Antinodes are the points where the maximum amplitude will be generated. At nodes, the two waves cancel out stopping the oscillation. Where are the antinodes and nodes at the bat? The node is at the sweet spot and the antinode is at the head and the mid-point of the bat.

It is interesting to note that due to the difference in the frequencies, the sounds differ depending upon where the ball hits the bat. One outfielder reportedly said that you can use the sound of the bat to determine how he would respond. He would run back towards the fence if he hears a "crack" (high frequency) and he would run in if he hears a "thunk" (lower frequency).

Is it just a coincidence that the sweet spot is at the node? No. The more that bat oscillates, more energy is wasted through it. So the maximum output is generated when there are no oscillations, at the nodes.