In a transverse wave, the crest or peak corresponds to a rarefaction or trough in a longitudinal wave. This is because the crest of a transverse wave represents the maximum displacement of the wave from its equilibrium position, while in a longitudinal wave, this corresponds to a region of high pressure or compression. Conversely, the trough or valley of a transverse wave corresponds to a region of low pressure or rarefaction in a longitudinal wave, where the particles are displaced away from their equilibrium position.
It's important to note that transverse waves and longitudinal waves are two different types of waves with different characteristics, even though they both involve the propagation of energy through a medium. Transverse waves are characterized by vibrations perpendicular to the direction of wave propagation, while longitudinal waves are characterized by vibrations parallel to the direction of wave propagation. Examples of transverse waves include light waves and water waves, while examples of longitudinal waves include sound waves and seismic waves.