  The propagation of linear transverse waves along a thin isothermal magnetic
flux tube is affected by a global cutoff frequency that separates propagating
and non-propagating waves. In this paper, wave propagation along a thin but
non-isothermal flux tube is considered and a local cutoff frequency is derived.
The effects of different temperature profiles on this local cutoff frequency
are studied by considering different power-law temperature distributions as
well as the semi-empirical VAL C model of the solar atmosphere. The results
show that the conditions for wave propagation strongly depend on the
temperature gradients. Moreover, the local cutoff frequency calculated for the
VAL C model gives constraints on the range of wave frequencies that are
propagating in different parts of the solar atmosphere. These theoretically
predicted constraints are compared to observational data and are used to
discuss the role played by transverse tube waves in the atmospheric heating and
dynamics, and in the excitation of solar atmospheric oscillations.
