The A stands for ‘weighting of the sound with an A-filter’.
A sound level meter with a ‘flat’ frequency response will measure the strength of a sound with a low pitch (e.g. 100 Hz) in the same way as the sound with a high pitch (e.g. 1000 Hz).  However, for the human ear, the low pitch sounds softer.  The eardrum, together with the hammer, stirrup and the oval window act as a mechanical filter with a determined frequency band. The ‘-3 dB’ frequencies of this filter measure 500Hz at the low side and 8000Hz at the high side. (-3 dB means that the experienced sound level of these frequencies has been halved.)  This is why with sound level measurements one often uses an electronic filter whose response to frequency is a bit like that of the human ear.  This way, the sensitiveness of the human ear is taken into account.  This frequency sensitiveness is different for high and low noise levels, but in almost all measurements and legislation the A-weighting is used to keep things univocal. 

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