Chapter 51: Waves – Shock, Bow & Surface Phenomena

Waves – Shock, Bow & Surface Phenomena provides a quantitative and qualitative investigation into diverse wave phenomena, commencing with an analysis of bow waves. These waves, which are often called shock waves when dealing with sound, are produced when a source moves through a medium faster than the speed of the wave itself. This speed differential results in a persistent wavefront that forms a cone in three dimensions, and the resulting angle of the cone is solely dependent upon the ratio of the wave speed to the source's speed. This principle is observed in phenomena such as Čerenkov radiation, where light is emitted when charged particles move through a transparent material faster than the speed of light within that material. The discussion then focuses specifically on strong shock waves, explaining that for disturbances with large amplitudes, the wave speed is directly influenced by the amplitude. High pressure created by the front of the wave actually speeds up the local wave velocity, causing the following parts of the wave to catch up to the front, which leads to the formation of a steep, sharp discontinuity. The physics of these extreme shocks indicates that they involve a significant loss of energy, appearing as a consequence of internal processes like heating. The third major section covers waves in solids, establishing that elastic media can support two distinct types of waves: compressional (longitudinal) waves, where particle motion is parallel to the wave direction, and shear (transverse) waves, where motion is perpendicular and which possess the unique property of polarization. The analysis of seismic waves created by earthquakes proves invaluable for mapping the Earth's interior. A critical deduction drawn from seismic data is that the Earth’s core must be liquid, because transverse waves are observed to cease propagation at the center. Finally, the chapter addresses surface water waves. It explores how wave speed is dictated by the relative influence of two different restoring forces: gravity (dominant for long waves) and surface tension (dominant for short ripples). This competition between forces leads to a minimum possible speed for water waves. Crucially, the chapter highlights the necessary distinction between phase velocity (the speed of a single crest) and group velocity (the speed at which the overall energy or pattern of the wave moves), explaining why a boat's wake pattern is a consequence of these two speeds being unequal.