To get a response in 'real time', you need to hear the volume change within 100ms or so of hitting the volume adjust picker or spinner or whatever. 8000 samples a sec is 8 samples in a ms, so if you process 800 sample chunks of the stream and shift each sample it left or right a bit to raise or lower the volume by 6dB, it might be good enough. To get 1 db steps, you'll need to multiply every sample by an attenuation factor from a db table.
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