Facts about waves A wave is any disturbance that transmits energy through matter or empty space.Most waves transfers energy without a medium. A medium is a substance through which a wave can travel. The transverse waves means moving across. In the longitudinal wave the particles of the medium vibrate back and forth along the path that the waves move. The amplitude of a wave is relates height. Frequency is the number of waves produced in a given amount of time. Compressions and rarefactions are like the crests and troughs of a transverse wave. The highest point in a transverse wave is called crest. The lowest point between each crest is called a trough.