- It is wrong to think the centers of compressions / rarefactions
of a longitudinal traveling wave are the counterparts of the
crests/ troughs of a transverse traveling wave. They are not because the displacements of the particles at the former
are zero while those at the latter displace from thier equilibrium positions the most.
- Besides, particles at centers
of compressions (rarefactions) have the greatest speed, and moving in
the same (opposite) direction of the wave propagation. Particles at the
crests / troughs of a transverse traveling wave are momentarily at rest.
- Actually, the compressions / rarefactions of a longitudinal wave correspond to the two "steepest hillsides" of a transerse wave.
- In the figure below, the direction to the right (left) in the longitudinal wave is transformed to upward (downward) direction in the tansverse wave.