In physics, the phenomenon of waves is one of the ubiquitous forms of motion in nature. Among them, longitudinal wave and transverse wave are two basic types of waves, each with unique propagation characteristics and physical properties. They correspond to the movement patterns of particles in the medium along the direction of propagation and perpendicular to the direction of propagation, respectively.
First of all, longitudinal w**e is a special type of wave characterized by the fact that each particle in the wave vibrates in the direction of the wave's propagation. Take sound waves as an example, in the air, sound waves are typical longitudinal waves, and air molecules will vibrate back and forth periodically in the direction of the sound waves. In an infinitely homogeneous medium, when the longitudinal wave propagates, the vibrational direction of the particle remains parallel to the propagation direction of the wave, that is, perpendicular to the wave front. This means that in the area through which the longitudinal wave passes, the volume of each point of the medium will change periodically, sometimes sparse, sometimes dense, so the longitudinal wave is also called "dense wave" or "expansion wave". In addition, another significant feature of longitudinal waves is that the curl field of the particle displacement vector is always equal to zero, which makes the longitudinal wave be named "no rotation wave", which further reveals the essence that there is no rotational component in the longitudinal wave propagation process.
On the other hand, transverse waves (transverse w**e) exhibit very different motion characteristics. In the process of transverse wave propagation, the direction of particle vibration in the medium is perpendicular to the direction of wave propagation. For example, sound waves exhibit the characteristics of transverse waves in some propagation media, in which the particles do not move with the waves, but vibrate laterally around their equilibrium positions. It is important to note that shear waves can only propagate in shear-elastic media, which limits the fact that shear waves are mainly present in highly viscous liquids and solid media. In the area where the transverse wave reaches, the divergence field of the displacement vector of the particle is zero, which means that there is no change in volume at each point of the medium, only tangential deformation, that is, the distance between the particles changes periodically, but the overall volume remains the same. Based on this characteristic, transverse waves are figuratively called "equal-volume waves", "shear waves", or "deformed waves".
In summary, although the two wave forms of longitudinal wave and transverse wave can carry energy and transmit information, there are significant differences in the propagation mode, the influence on the medium, and the vibration characteristics of the particle. Understanding the different properties of these two types of fluctuations is of crucial significance for understanding the various wave phenomena in nature and even for solving many problems in the field of engineering and technology.