The animations top top this page highlight the vibrational habits of a baseball bat. I have an additional website which includes much more information around the physics and acoustics of baseball bats, with lots of graphs, data, animations, and also some conversation of the physics behind the wood-aluminum-composite debate.

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Bending Modes

A openly supported baseball bat exhibits several flexural bending settings of vibrtation which are similar to those that a free-free beam. One could be skinny to think that a hand-held bat need to be treated an ext like a clamped-free (cantilever) beam. However, research has shown<1> the while the hands quickly damp the bat vibrations, a hand organized grip (even tightly gripped) does not significantly adjust the vibrational frequencies or the modeshapes. The frequencies and also shapes because that a bat which is complimentary at both ends, sufficiently define the vibrational habits of a hosted bat.The animations at right display the an initial four bending settings of a baseball bat. Actually the animations were developed from speculative data obtained for a Louisville Slugger Genesis sluggish pitch softball bat, a hollow barrel bat do from carbon fiber composite materials. However, the vibrational shapes and the node locations are very comparable to those for solid wood and aluminum baseball/softball bats I have actually tested in the acoustics laboratory at Kettering University. The first bending setting usually occurs at a frequency roughly 170Hz and also is extremely important to the performance of a bat. Among the meanings of the \"sweet spot\" is the location of the node at the barrel finish of the bat. This point, generally 5-7 inches from the barrel end, does not move when the bat is vibrating in its an initial (or fundamental) bending mode. One more node exists about 6 inches native the handle end (both nodes are established by the black color dots in the animation). An impact at the node will certainly not reason the bat to vibrate, and thus nobody of the initial power of the round will be lost to the bat. In addition, the player will not feel any kind of vibration at this frequency.The 2nd bending mode, typically occuring close to 600Hz, is also an extremely important together it likewise has a node about 2-3 customs from that of the very first bending mode. A \"sweet zone\" is often defined as the region between the nodes of the an initial two bending modes.<2> An influence in region will minimally exite the an initial two bending modes, for this reason the player will feel little vibration and also the ball will no lose energy to bat vibration.The higher bending settings probably have small influence top top the feeling of the bat, but computer calculations have displayed that lock can considerably influence the post-impact ball speed.

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First Bending Mode
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Second Bending Mode
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Third Bending Mode
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Fourth Bending Mode
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Hoop Modes

A solid wood bat will only vibrate with bending movement (torsional motion?). A hole aluminum or composite bat, however, is able come vibrate with another class of setting shapes in i beg your pardon the hollow cylindrical barrel that the bat oscillates.
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The animation at left shows how the cross-section the the barrel alternately compresses and expands in perpendicular directions. The animations at right display the vibration the the top and also bottom the the barrel while viewing the bat from the side.The an initial hoop setting is responsible for both the \"trampoline effect\" and the \"ping\" sound of one aluminum bat. Because that most solitary walled aluminum bats this mode has actually a frequency approximately 2000Hz; because that most double walled aluminum bats that is about 1500Hz; and for some recent composite bats it is together low together 1000Hz. This vibrational form radiates sound in a quadrupole sample - quadrupoles are quite inefficient sound radiators, but the frequency (2000Hz) is in the variety of sounds many readily heard by the human ear so the \"ping\" deserve to sound fairly loud. In fine designed bats this very first hoop setting shapes is as broad (long) as feasible and the place of best displacement synchronizes to the node of the first bending mode (indicated through the red dot). A ball impact at the sweet spot will certainly excite the hoop mode but not the bending vibrations. Much effort has entered trying to make the most use of the trampoline effect. My current research says that tuning the first hoop setting to a particular frequency may significantly enhance the trampoline effect and the resulting round speed.The 2nd hoop mode is of less importance, and also will it is in minimally excited by a hit near the sweet spot because there is a node (a circle around the circumference of the bat i m sorry does no vibrate) there. This mode is an extremely inefficient octupole type of sound radiator and will no be an extremely audible also if exited by a hit off the sweet spot. The third hoop setting is also less crucial to the performance of a bat.
First Hoop Mode
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Second Hoop Mode
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Third Hoop Mode
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computer version of the very first three cylinder (hoop) modes
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References<1> H. Brody, \"Models that baseball bats,\" American newspaper of Physics, 58(8), 756-758 (1990)<2> R. Cross, \"The sweet clues of a baseball bat,\" American newspaper of Physics, 66(9), 771-779 (1998)<3> L. L. V. Zandt, \"Thy dynamical concept of the baseball bat,\" American journal of Physics, 60(2), 172-181 (1992)<4> A. M. Nathan, \"The dynamics of the baseball-bat collision,\" American newspaper of Physics, 68(11), 979-990 (2000) ago to Acoustics and Vibration AnimationsForward come Physics and also Acoustics that Baseball/Softball Bats