Question

waves that require a medium

transverse waves mechanical waves

trough frequency

Explanation:

To determine which term matches "waves that require a medium", we recall wave definitions: Mechanical waves (like sound) need a medium (solid, liquid, gas) to travel. Transverse waves are a type of wave (oscillations perpendicular to direction, e.g., light is transverse but is electromagnetic, no medium needed; water waves are transverse mechanical). "Trough" is a part of a wave (low point), "frequency" is wave cycles per unit time. So mechanical waves require a medium.

Answer:

mechanical waves