Acoustic guitar strings when plugged vibrate back-and-forth. As they do, they increase and decrease in tension very rapidly. This causes the soundboard on the guitar to move up and down.
When this happens, the top of the guitar acts almost like a speaker cone, creating sound.
The purpose of the sound hole is to allow the top to vibrate as freely as possible, which increases the volume and quality of tone that you can create from the instrument.
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