  The scalar Klein-Gordon equation describes wave motion in a waveguide with a
cut-off. For example, the displacement of an elastic cord anchored to a solid
base by elastic elements can be described by the scalar Klein-Gordon equation.
We analyse this equation using the concept of analytical continuation of
dispersion diagram. Particularly, it is shown that the dispersion diagram is
topologically equivalent to a tube analytically embedded in two-dimensional
complex space. The corresponding Fourier integral is studied on this tube using
the Cauchy's theorem. The basic properties of the scalar Klein-Gordon equation
are established.
