Third sound in one and two dimensional modulated structures

An experimental technique is developed to study acoustic transmission in one and two-dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two-dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimensions. Nevertheless, we find that the transmission spectrum in the Penrose lattice, which is a two-dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained, in terms of dynamical theory of diffraction.