A longitudinal wave : is the disturbance in a medium due to vibration of particles in the direction parallel to the direction of propagation of the wave.
It is a periodic wave, having a wavelength, frequency and velocity of propagation. The distance between the successive points having the same phase is called the wavelength. The time duration for the wave to travel the wavelength is called the time period. Frequency is the number of times a particle oscillates in a second, or, the number of times a particle crosses its mean position in a second.
Sound wave is a longitudinal wave. A longitudinal wave needs a medium to propagate. It is also a mechanical wave. A longitudinal wave has compression regions in which there is an excess pressure, and rarefactions - regions in which there is low pressure.
Propagation of longitudinal wave depends on the bulk modulus of the medium ie., the elastic properties. In general, a denser and stronger medium propagates a longitudinal wave faster. All media have bulk modulus, so longitudinal waves propagate in all media.
Transverse waves :
This is a periodic wave in which the particles in the medium vibrate perpendicular to the direction of propagation of the wave.
The properties wavelength, time period, frequency and definitions of these quantities are same as those of longitudinal waves. Wavelength of a transverse is the distance between successive crests or troughs of the wave. Crest and troughs are the extreme positions in the vibration of a wave. The difference between a crest and its mean position is called the amplitude of the wave.
Visible Light wave, electromagnetic waves, standing waves on a wire fixed at one end or two ends - are all examples of transverse waves.
Transverse waves can be travelling waves or standing waves. Longitudinal waves are travelling waves. Transverse waves can propagate only in a medium which has shear modulus of elasticity. Not all media support transverse waves.
When transverse waves and longitudinal waves are reflected from a fixed or open boundary, the phase differences in the reflected waves could be different.
Transverse waves can be polarized. Polarization means the direction of oscillation or plane of oscillations can be changed. Longitudinal waves cannot be polarized. The plane of oscillations is fixed.