Bianca Violet and Stephan Klaus
Theoretical physicists call a drum a vibrating circular membrane.
The movement of the membrane is described by Bessel functions, which
are complicated, analytic functions that do not satisfy a polynomial
equation. In our short movie, we approximate and effectively
simulate different characteristic patterns (normal modes) of the
drum vibration using algebraic surfaces instead, which are given by
simple polynomial equations (in contrast to Bessel functions). The
patterns are characterized by lines or circles, which stay still,
while everything else is moving up and down. We show vibrations with
up to three such nodal lines and two circular nodal curves. This
visualization was created with the free SURFER software by
IMAGINARY. A manuscript on the math behind it is currently in
preparation and will be made available on the IMAGINARY platform.
All necessary formulas will be included to be able to create your
own algebraic vibrations.