A
transverse wave is one where the
vibration at any point is
perpendicular to the direction of travel of the
wave. Familiar examples include
ocean waves,
electromagnetic waves, and plucked
strings. Contrast with
longitudinal waves, where the direction of vibration is the same as that of wave motion.
In an ocean wave the water molecules move up and down, and a cork floating on them will also, whereas the pattern of wave crests and troughs moves forwards, and transmits energy across distance. In mechanical waves, whether in water or strings, it is the displacement of particles that oscillates. In an electromagnetic wave it is the strengths of the electric field and magnetic field at a point that oscillate. Oscillations may be along any angle of the 360° plane that is perpendicular to the wave direction, but if they lie along a single line of that plane then the wave is polarized, of which the most familiar example is polarized light.
The velocity of a transverse wave in a string is given by v = sqrt(T / m), where T is the tension and m is the mass per unit length.
The velocity of EM waves in a medium is given by v = sqrt(1/με), where μ is the permeability of the medium and ε is its permittivity. In vacuum these are called the permeability and permittivity of free space and symbolized μ0 and ε0. The fact that EM waves can be polarized shows that they must be transverse, not longitudinal.