Q1. A fan at a rock concert is 30 m from the stage, where sound intensity level is 110 dB. Her eardrums have the diameter of 8.4 mm. How much energy is transferred to each eardrum in one second? (Distance from the speaker to the edge of the stage is 1 m.)
Q2. A uniform density cube of mass m, side 2b, and center at C is placed on a fixed horizontal cylinder of radius r and center O in Earth's gravitational field. The cube is originally put so that C is centered above O, but it can roll from side to side without slipping. Use the Lagrangian approach to find out an angular frequency of small oscillations about the top position. Note the moment of inertia of cube I = 2mb2/3 and for the small angle approximation: sin θ ≈ θ and cos θ ≈ 1 - θ2.