Sound is sound waves, similar to waves in the water.
The device creates sound by sending electricity to a speaker. The electricity pushes the speaker inwards or outwards, creating a larger or smaller wave, depending on how much electricity you send through.
To make it quieter, the device simply sends less electricity. This can be done in multiple ways, e.g. changing the amplification in an amplifier circuit, or just taking the sound wave that it is trying to play, and multiplying it by the volume percentage.
A electronically recorded sound wave consists of a series of numbers. Each number says how much power to send to the speaker at a specific time. The is one number for (typically) every 1/44100th of a second. So if you set the volume to 10%, it simply multiplies each number with 10% (= 0.1) to determine how much power to actually send to the speaker.
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