A cavity back golf club head having a bridge member and a damping element is disclosed. The bridge member extends across a first rear cavity connecting a heel and a toe of the golf club head to control the trajectory of a golf ball. For the longer iron clubs, a damping element extends from the sole portion of the cavity back golf club head to the bridge member to define a second cavity to further influence the trajectory of the golf ball. For the shorter iron clubs, the damping element extends from the top portion of the cavity back golf club head to the bridge member. The damping element may reduce the vibration and sound of the golf club head upon impact with a golf ball.