The propagation of elastic waves in inhomogeneous media has attracted much attention over the last years. Media with periodically varying elastic coefficients are called phononic crystals. Phononic crystals can be the siege of complete acoustic band gaps. For frequencies within a complete band gap, there can be no vibration and no propagation of acoustic waves, whatever the polarization and the wave vector. In such a situation, a phononic crystal behaves like a perfect mirror and can be further modified to gain control over acoustic waves. This principle can be used to obtain acoustic cavities, acoustic filters, or very efficient waveguides by adding certain defects to the lattice. All these functions can be achieved in a very tight space of the order of the acoustic wavelength. The purpose of this paper is to demonstrate a complete band gap in a phononic crystal slab and to investigate the propagation of acoustic waves within it. The system we have chosen is a finite thickness, solid/solid and two face free phononic crystal slab. This system lends itself to numerical simulation by a finite element method developed previously. Furthermore, by using a combination of ultrasonic electrical transduction and optical detection by a laser interferometer, we can obtain a map of the propagation of waves at any monochromatic frequency. This experimental set-up is used to quantify the attenuation on propagation and the confinement of acoustic energy within a linedefect waveguide. A complete band gap was identified by measuring the transmission spectrum along the two most symmetric directions of the Brillouin zone by laser interferometry. The measured transmission spectra and the theoretical band structure obtained by a finite element method are in agreement and show that the complete band gap ranges from 255 kHz to 340 kHz. The dependence of the attenuation on the propagation distance was studied. Little attenuation is observed below the complete band gap and a clear exponential decay is observed within it. Unexpectedly, a pronounced unexpected decay is observed for frequencies above the complete band gap, unlike observations for bulk acoustic waves. Finally, a defect line waveguide was formed. The transmission through the waveguide was measured and the wave field was imaged. The observations show that the waveguide confine the acoustic energy within the complete band gap.