The type of wave where particles of the medium vibrate to and fro in the same direction as the wave propagation is called a longitudinal wave.

Here's why:

* Longitudinal waves: The particles in the medium oscillate parallel to the direction the wave travels. Think of a spring: when you compress one end, the compression travels down the spring, causing the coils to move back and forth in the same direction as the wave.

* Transverse waves: In contrast, transverse waves have particles that vibrate perpendicular to the direction of wave propagation. Imagine a rope tied to a post: when you shake it up and down, the wave travels along the rope, but the rope itself moves up and down, perpendicular to the direction of the wave.

Examples of longitudinal waves:

* Sound waves

* Seismic P-waves

Let me know if you have any other questions about waves!