Here's why:
* Transverse Wave: In a transverse wave, the particles of the medium oscillate perpendicular to the direction the wave travels. Think of a wave on a string. The string moves up and down (perpendicular), while the wave itself travels horizontally.
* Particle Velocity: The particle velocity is the speed at which the individual particles in the medium are moving. In a transverse wave, this velocity is always perpendicular to the direction of wave propagation.
* Wave Velocity: The wave velocity is the speed at which the disturbance (the wave) itself travels through the medium.
Therefore, the angle between the particle velocity and the wave velocity in a transverse wave is 90 degrees (or a right angle).