Technical ReportPDF Available

Comparison of different techniques of thermal modification, regarding the improvement of acoustical properties of resonant soundboard material Scientific Report by order of Pacific Rim Tonewoods Inc

Authors:
  • Eberswalde University for Sustainable Development

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Content may be subject to copyright.
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The damping constants of the first bending modes changed differently for the
longitudinal (mode2) and the radial (mode4) motion. In general there were small
changes for the damping and the variation was very high, although significant shifts
were detected. For a longer sound fade out and a higher reflection of the induced
energy at the guitar, a lower damping is requested. For the longitudinal bending mode,
this could be achieved from the treatments 2 and 3. Process 1 did not change
significantly and 4 and 5 increased the damping slightly. The radial bending vibration
was stronger affected (fig.29/31). All treatments decreased the damping. The highest
reduction of vibration energy absorption was measured on samples of treatment
number 3 in both directions.
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Agents and Moisture Content on Ultrasonic Pulse and Resonant Vibration. Holzforschung 51: 11-20
Machek, L, Militz H, Sierra-Alvares R (2001) The use of an acoustic technique to assess !wood decay in
laboratory soil-bed tests. Wood Sci. Technol. 34(1): 467-472 !
Grinda M, Göller S (2005) Some experiments with stake tests at BAM test field and in the BAM fungus cellar.
Part 2: Comparison of static and dynamic moduli of elasticity (MOE). !International Research Group on Wood
Protection IRG/WP 05-20320 !
Görlacher, R. (1984) Ein neues Messverfahren zur Bestimmung des Elastizitätsmodulus von !Holz. Holz als Roh-
und Werkst. 42: 219-222 !
Ono T (1996). Frequency responses of wood for musical instruments in relation tot he vibrational properties.
Journal of the Acoustic Society of Japan 17: 183 !
Fengel D, Wegener G (2003) Wood. Chemistry, Ultrastructure, Reactions. Verlag Kessel!
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