Which mode of vibration has the greatest velocity when all other factors are equal?

The longitudinal wave is characterized by particles in the medium moving back and forth in the same direction as the wave travels. This direct particle motion along the direction of wave propagation allows longitudinal waves to transmit energy with a higher velocity compared to other types of waves, such as transverse or surface waves, when all other factors are equal.

In a longitudinal wave, since the particles move in the direction of the wave, they can effectively transmit energy through compressions and rarefactions, enabling a more efficient and faster transfer of energy across the medium. This results in a greater velocity of the wave itself.

Transverse waves, while they can carry energy effectively, require a medium that can support shear forces, which typically limits their speed compared to longitudinal waves in a solid. Surface waves, which include Rayleigh waves, propagate along the surface of a medium and generally have lower velocities because they involve both longitudinal and transverse motion, and energy is lost to the medium deeper than the surface level. Rayleigh waves specifically combine both types of motion, resulting in even slower propagation speeds than pure longitudinal waves.

Understanding the relationships between wave types and their velocities helps clarify why longitudinal waves are superior in terms of speed in this context.