  We study a periodic vibrating string composed of a finite sequence of string
segments connected periodically, with each segment characterized by a constant
linear mass density. The main purpose is to provide a configuration that can
mimic the properties of photonic or phononic crystals and could be implemented
in undergraduate physics laboratories. We demonstrate that this configuration
displays frequency intervals for which wave propagation is not allowed
(frequency bandgaps), in close analogy to photonic and phononic crystals. We
discuss the behavior of these bandgaps when varying physical parameters, such
as the values of the linear mass densities, the oscillation frequency, and the
number of strings constituting the entire system. Some analogies with the
propagation of electronic waves through a crystal lattice in condensed matter
physics are also explored.
