The ongoing expansion of the frequency range used for ultrasonic imaging requires increasing attention to the acoustic attenuation of biomaterials. This work presents a novel method for measuring the attenuation of tissue and liquids in vitro on the basis of single transmission measurements. Ultrasound was generated by short laser pulses directed onto a silicon wafer. In addition, unfocused piezoelectric transducers with a center frequency of 50 MHz were used to detect and emit ultrasound. The laser ultrasound method produces signals with a peak frequency of 30 MHz. In comparison to piezoelectric generation, pulse laser excitation provides approximately 4 times higher amplitudes and 20% larger bandwidth. By using two excitation methods in succession, the attenuation parameters of porcine fat samples with thicknesses in the range of 1.5 to 20 mm could be determined quantitatively within a total frequency range of 5 to 45 MHz. The setup for liquid measurements was tested on samples of human blood and olive oil. Our results are in good agreement with reports in literature.