Tech Note 1141 Detail

Wave Motion Demonstrator Calculations

Affected Products:

SE-9600 Complete Wave Motion Demonstrator

Problem/Symptom:
Wave Motion Demonstrator Calculations

PASCO Solution:

Wave Motion Demonstrator Constants and Calculations

  • Short rods
    • mass m = 21.8 g
    • length L= 228 mm
    • Moment of Inertia Ibar=m L2/12 = 9.44E-05 kg m2
  • Long rods
    • mass m = 43.2 g
    • rod length L= 45.7 cm
    • Ibar= 7.52E-04 kg-m2
  • Inter-bar
    • torsion spring constant k = 1.03 N-m/rad
    • separation = 12.65 mm
  • Wave Speed v = sqrt(k/I)
    • Wide section
      • Vcalculated = 0.47 m/s
      • Vmeasured = 0.51 m/s
    • Narrow section
      • Vcalculated = 1.32 m/s
      • Vmeasured = 1.45 m/s
  • Characteristic Impedance Z = sqrt(k*I)
    • Zwide = 0.0278 N-m-s
    • Znarrow= 0.0099 N-m-s
  • Reflection and Transmission Coefficients
    • Reflection Coefficient R12 = (Z1-Z2)/(Z1+Z2)
      • Rwide-narrow = 0.48
    • Transmission Coefficient T12 = 2*Z1/(Z1+Z2)
      • Twide-narrow = 1.48
    • Note: If unit is not terminated (Z2 = 0), then R12 = 1, corresponding to full reflection without a phase change.
    • If the last bar is clamped (Z2 -> infinity), then R12 = -1, corresponding to full reflection with inversion of phase.

Creation Date: 05/4/2011
Last Modified:
Mod Summary: