We show how well-known in physics parametric resonance affects global in time existence of the solution to the nonlinear wave equation. Namely, assume that in the nonlinear wave equation (with large dimension of spatial variable), which for sufficiently small initial data possesses the global in time solution, one allows a small periodic in time perturbation in the speed of propagation (coefficient). Then we prove that there are arbitrary small initial data, which produce a solution blowing up in the finite time. We point on the close relation of this phenomenon to the theory of the operators with multiple characteristics.