  The dispute about the well-known 1D vibrating string model and its solutions,
known as The Vibrating String Controversy, spanned the whole of 1700s and
involved a group of the most eminent scientists of the time. After that, the
model stood undisputed for over two centuries. In this study, it is shown that
not only this 300-year-old model cannot correspond to reality, but it is
theoretically not quite plausible, either. A new 2D model is developed removing
all the assumptions of the classical model. The result is a pair of non-linear
partial differential equations modeling 2D motions of a finite 1D string. A
theorem that can be used to determine the initial displacement functions from
the initial shape of the string is proven. The new model is capable of
representing initial conditions that cannot be handled in the classical model.
It also allows initially non-taut/non-slack strings and self-intersecting
shapes. The classical model and the non-taut strings emerge as special limit
cases. It is proven that pure transverse motions of a 1D string are possible
only in very rare cases. A theorem that sets the conditions for pure transverse
motions is also presented. Numerical studies of interesting cases are presented
in support of the new model. High-speed camera experiments are also conducted,
the results of which also support the new theory.
