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Transverse vs longitudinal modes on a 1D chain

What you are seeing: a 1D chain of masses connected by springs supports both transverse waves (particles bob perpendicular to the chain) and longitudinal waves (particles compress along the chain). Both share the dispersion relation ω(k)=2K/m∣sin⁡(ka/2)∣\omega(k) = 2\sqrt{K/m}|\sin(ka/2)|.

Figure 1. Both modes shown with the same dispersion; the difference is in the polarization direction.
k (1/a)1.0
amplitude0.20
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WHAT TO TRY

  • Vary each control and watch the rail readouts respond.
  • Compare the diagnostic plot against the live scene.