The present study discloses the evaluation of second-order elastic constants of wurtzite boron nitride(w-BN) at room temperature and at different pressures using the many-body interaction potential model approach. Orientation- and pressure-dependent ultrasonic velocity, thermal relaxation time and other related thermophysical parameters (Debye temperature, Debye average velocity, specific heat and thermal energy density) are also calculated using the evaluated second-order elastic constants. The orientation-dependent thermal relaxation time of w-BN is predominantly affected by the Debye average velocity and is indirectly governed by second-order elastic constants. Thermal relaxation time of w-BN is found to decrease with pressure. Calculated elastic and ultrasonic properties of w-BN are compared with the properties of other wurtzite structured materials for a complete analysis and characterisation of the material.