Chapter 9: Wave Equations

Waves occur in many aspects of our daily lives and in the nature which surrounds us. Just take a stone and throw it into a resting water surface: you will observe a surface wave, spreading in concentric circles around the impact point on the water. Or think of the high breaking waves in the ocean which are so highly desirable for surf champions. Less pleasantly, there are the energy waves generated by potent seaquakes, which travel under the ocean surface with the speed of about thousand kilometres per hour and turn into deadly tsunami water waves close to beaches. Other examples are the sound waves, generated by our speech, propagating in the air to the partner of our conversation, electromagnetic waves described by the Maxwell equations, light propagating in spherical waves from a source and, even more fundamentally, as established by quantum mechanics [16] , there is a matterwave duality which basically states that even particles with positive mass (say, electrons) have wave-like features (e.g. delocalisation). So how is wave motion characterized? Webster’s dictionary gives the following definition: