Question

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mechanical wave
longitudinal wave
transverse wave
requires a material in order to move between locations.
this type of wave can move through a vacuum.
electromagnetic wave
particle motion and wave motion are parallel to each other.
particle motion and wave motion are perpendicular to each other.
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Explanation:

Step1: Recall wave definitions

Mechanical waves need a medium (material) to travel. Electromagnetic waves can travel through vacuum (like light). Longitudinal waves have particle motion parallel to wave motion. Transverse waves have particle motion perpendicular to wave motion.

Step2: Match each term

• Mechanical Wave ↔ Requires a material in order to move between locations. (Mechanical waves need a medium.)
• Electromagnetic Wave ↔ This type of wave can move through a vacuum. (Electromagnetic waves don't need a medium.)
• Longitudinal Wave ↔ Particle motion and wave motion are parallel to each other. (Definition of longitudinal waves.)
• Transverse Wave ↔ Particle motion and wave motion are perpendicular to each other. (Definition of transverse waves.)

Answer:

• Mechanical Wave - Requires a material in order to move between locations
• Electromagnetic Wave - This type of wave can move through a vacuum
• Longitudinal Wave - Particle motion and wave motion are parallel to each other
• Transverse Wave - Particle motion and wave motion are perpendicular to each other