The effect of wood grain on vibrational modes of a wood bat

Wood bats manufactured for amateur and youth players are not made from the same quality of wood as those made for professional players. As a result, a wide range of wood properties may be found in a collection of bats which are otherwise the same (same model, length, profile). At a local sporting goods store I found two Little League wood bats which exhibited quite different acoustical behavior. Both bats are Louisville Slugger models 225YB and have identical lengths, barrel diameters and profiles. But, one bat weighs 26-oz and has 8 wood layers (grain density) per inch and the other bat weighs 20-oz and has 20 wood layers per inch. Optimal grain density is around 6-10 layers per inch, though it is possible for two wood samples with 3-5 layers per inch or 12-20 layers per inch to have similar properties.^[2]

While setting up one of the modal analysis experiments I discovered that when I tapped the bat at the barrel end I heard different frequencies depending on whether I tapped it along (parallel to) the grain or across (perpendicular to) the grain. The change in pitch was very audible. I quickly checked the other wood bats in the lab and found that most of them showed the same effect - the frequencies were different for the two directions. For most of the wood bats I tested, the frequencies along the grain were higher than those across the grain. Once I thought about it, this effect did not surprise me. Wood is an anisotropic material, which means that the elastic constants, and thus the wave speed, depend on direction.[3] The wave speed along (parallel to) the grain is lower than the wave speed across (perpendicular to) the grain, so the frequencies should be higher when the bat is tapped along the grain in the direction you want to the ball to hit. The figure at right shows typical frequency response functions for impacts along and across the grain. Each peak in the plot represents a bending mode, and the plot shows very effectively how the two orientations split in frequency. The split is more pronounced for the higher bending modes. After some experimentation I determined that the audible pitch change was due to the frequencies for the second bending modes. The worst bat had an audible 25 Hz difference centered at about 700 Hz, a difference almost corresponding to a musical half step. What did surprise me was that I found two bats for which the frequency perpendicular to the grain was lower than the frequency parallel to the grain, exactly the opposite of what I would have expected. I did find two Little League bats, one ash and the other maple, which were both hand carved from quality wood (I had to special order them) which had no audible difference in frequency and which showed very little mode splitting even for the higher bending modes. What effect does this mode splitting have on a bat's performance? My guess that the primary effect, if any, would be in the perception of feel, especially for hits which are not directly aligned with the wood grain. . The middle figure at right shows the frequency spectrum measured by a mirophone for an impact at 45o to the grain. When the impact is aligned with (parallel to) or perpendicular to the grain only one frequency is heard. But when the impact is at an angle, both frequencies are excited equally and a strong beat frequency is heard. The bottom figure at right shows the vibration response at the handle of the bat, measured with an accelerometer, for an impact at 45o at the barrel end. The beat frequency is observed as the envelope of the vibration signal (think of the "wah-wah-wah" pattern for a beating sound). A player who is holding the bat will feel this beat pattern. The hands are most sensitive to vibrations with frequencies below 200 Hz.[4] Since this beat pattern is around 25Hz it would be very noticeable. It is true that the hands damp out the bat vibration very quickly (within a few tens of milliseconds), but the impulse felt as a "sting" for a bat hit may be exacerbated by a bat with this mode splitting beat phenomena.

Frequency Response Functions for impacts parallel to the grain (solid curve) and perpendicular to the grain (dashed curve). Microphone response for an impact at 45o to the grain direction. Beat pattern, measured with an accelerometer at the handle of a bat for impact at 45o to the grain at the barrel end.

[1] T. Herr, "The Good Wood," Sports Illustrated, 64(15), 66-80 (April 14, 1986)
[2] S. Ashley, "Getting Good Wood (or Aluminum) on the Ball," Mechanical Engineering, 112(10), 40-47 (1990)
[3] V. Bucur, Acoustics of Wood, (CRC Press, New York, 1995)
[4] D. D. Reynolds, K. G. Standlee, and E. N. Angevine, "Hand-arm vibration: Part III. Subjective response characteristics of individuals to hand-induced vibration," Journal of Sound and Vibration, 51(2), 267-282 (1977)
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