Sound is a mechanical wave, meaning it needs a material medium (such as air, water or a solid) to travel and cannot pass through a vacuum. More specifically, sound in air is a longitudinal wave, and the defining feature of a longitudinal wave is the relationship between the motion of the medium's particles and the direction the wave travels.

Why the correct description is that air particles vibrate back and forth parallel to the wave direction: When a source such as a vibrating tuning fork or loudspeaker pushes on the surrounding air, it sets neighbouring air molecules oscillating along the same line in which the wave moves. This produces alternating regions of compression (where particles bunch together, creating high pressure) and rarefaction (where particles spread apart, creating low pressure). These compressions and rarefactions travel outward as the sound wave. Importantly, the individual air particles do not travel with the wave — they merely oscillate to and fro about their fixed average positions, passing the energy along from one particle to the next.

Why the other options are wrong:

• Particles vibrating perpendicular (up and down) to the wave direction describes a transverse wave, such as light or waves on a string — not sound in air.
• Moving in circular paths describes the motion of particles in surface water waves (which are a combination of longitudinal and transverse motion), not the straight-line oscillation of sound in air.
• Particles remaining stationary while the wave passes is impossible, because a mechanical wave transports energy precisely by making the medium's particles vibrate; without particle motion there would be no sound at all.

Therefore, sound travels through air as a longitudinal wave in which the particles oscillate back and forth parallel to the direction of propagation.