Electromagnetic waves are, as the name may imply, not sound waves. Waves do not actually require a medium to exist in. Only mechanical waves, a specific subset of waves including sound and gravity waves (not *gravitational* waves, but waves caused by gravity like water waves) requires a medium to travel through.
Light waves exist independent of a medium – they are fluctuations in the local electric and magnetic fields, which perpetuate themselves outwards indefinitely.
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