Two-dimensional turbulent flows past a square cylinder and cavity noise are simulated by the finite difference lattice Boltzmann method with subgrid turbulence model. The method, based on the standard Smagorinsky subgrid model and a single-time relaxation lattice Boltzmann method, incorporates the advantages of FDLBM for handling arbitrary boundaries. The results are compared with those by the experiments carried out by Noda & Nakayama and Lyn et al. Numerical results agree with the experimental ones. Besides, 2D computation of the cavity noise generated by flow over a cavity at a Mach number of 0.1 and a Reynolds number based on cavity depth of 5000 is calculated. The computation result is well presented a understanding of the physical phenomenon of tonal noise occurred primarily by well-jet shear layer and vortex shedding and an aeroacoustic feedback loop.