We report measurements of the temperature and pressure dependence of ultrasonic modulus and specific volume in polystyrene between 50 and 280 degrees C and applied pressures up to 775 bar. The volumetric glass transition temperature is found to vary linearly with pressure. Furthermore, it coincides with the temperature at which the velocity of sound and the attenuation in the material show pronounced change from solid-like to liquid-like behavior. The storage and loss moduli are analyzed within the Havriliak-Negami model and very good agreement is found over the entire temperature and pressure ranges. Using the Vogel-Tammann-Fulcher equation for the relaxation time, the Kauzmann temperature T-k and the fragility parameter D of polystyrene were determined from fits to the data. T-k is also a linear function of pressure, but D is constant over the whole pressure range. The value of D allows us to classify polystyrene among the fragile-glass formers.