In this thesis, a femtosecond pump-probe laser setup is used to study GHz acoustic waves in suspended phononic crystal (PnC) waveguides. These membranes consist of 200 nm thick Si3N4 coated with a 20 nm gold film and shamrock shaped PnCs. Various COMSOL simulations of these waveguides are conducted to investigate the expected behavior of the membranes. These simulations not only reveal the eigenmodes and phononic bandgaps of two different membranes, but also show the formation of a 300 MHz Lamb wave inside the waveguide. Experimental results show that this 300 MHz Lamb wave is confined inside the waveguide, when the frequency of the Lamb wave falls within the phononic bandgap of the membrane. For membranes with a bandgap that does not include the frequency of the Lamb wave, propagation through the PnC lattice is seen. Finally, an Acousto Optic Modulator (AOM) is successfully integrated in the pump-probe laser setup to increase the frequency resolution of the measurements. The experimental data obtained with this higher frequency resolution shows similar results of wave confinement and proves repeatability of the measurements.