Question

what do sound waves move or travel through

Answer 1

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Sound waves traveling through air are indeed longitudinal waves with compressions and rarefactions. Assound passes through air (or any fluid medium), the particles of air do not vibrate in a transverse manner.
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$\orange{hope\:it\:helps}$

Answer 2

Sound Waves are nothing but disturbances in the particles of the air the energy is transferred from on one particle to another which transfer the waves through compressions and rarefactions in the particles of air.
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