An ear cup with a microphone apparatus including an inner cup portion, for forming a noise damping space, and an outer cup portion for forming a space for accommodating electronics and/or a current source. The inner cup portion and the outer cup portion are separated by a partition. The inner cup portion has a pocket and two opposingly located recesses in which a bracket for a microphone is disposed. Over the microphone, a windshield is provided, this protecting the microphone from being damaged and also damping wind noise. The windshield has an outer configuration that may be seen as a continuation of the outer cup portion, in order to prevent turbulence in the region of the windshield. The windshield is produced from a porous material, which is surrounded by a mounting frame having nap catches for engagement in snap catches.