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The determining factor as to the softness or loudness of a sound is the amplitude of the sound wave. We know that sound is mechanical energy, and a source of sound will put mechanical energy into the medium through which it is going to travel. Let's look at the wave.

The mechanical wave has a compression phase and a rarefaction phase. In compression, the source compresses the medium to impart energy. In the rarefaction phase, the source will act to decompress the medium. The sound will propagate outward in a series of compression and decompression phases.

The difference between a loud and a softer sound is the degree to which a medium is compressed and rarefied during the process by which the sound energy is put into the medium. Fortunately there is a question (and an answer) that goes into this in a bit of detail. It is linked in the Related questions section.

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Q: What determines if a sound is loud or soft?
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