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How does the volume level work in computers / phones / players?
The question probably sounds silly, but still.
Does lowering the volume in digital audio devices affect the "bit depth" of the sound wave?
Those. Does the volume work programmatically by changing the samples directly?
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A sound wave has no bit depth. The last place where "bit depth" plays any role in modern devices is a mixer, where signals from different sources are mixed digitally. From it, the signal goes to the DAC, which produces an analog signal fed to an analog amplifier. Its gain factor is also digitally regulated ... but this does not affect the "bit depth" of the signal itself .
However, if we talk about the subjective perception of sound quality, then the volume level certainly affects it, because. Any amplifier introduces noise and harmonic distortion into the signal.
In addition, between the amplifier and the ear there is also a speaker (passive, such as headphones, or even active, such as speakers with their own amplifier, separating filters, etc.) with its own frequency response, introduced distortions , etc. more or less adequately coordinated with each other components of household devices, the "maximum" sound quality is achieved at a volume level of 30 ~ 40%. But this is a very very general rule.
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