No, sound waves do not travel through empty space. Sound waves are mechanical waves that require a medium, such as air, water, or a solid material, to propagate. When an object vibrates, it creates disturbances in the surrounding medium, which then propagate as compressions and rarefactions, forming sound waves. These compressions and rarefactions cause particles in the medium to oscillate, transferring energy from one particle to another and carrying the sound wave forward.
In the vacuum of outer space, where there is no medium, sound waves cannot travel. This is because there are no particles to transmit the vibrations. However, in environments where a medium is present, such as Earth's atmosphere, water, or solids, sound waves can travel and propagate through them.