运用功能原理推导机械波的波动方程

A Derivation of the Wave Equation of Mechanical Wave by Principle of Power and Energy

机械波是机械振动在弹性介质中的传播,是物质运动的一种基本形式.现有波动方程的推导大多是从牛顿运动定律出发,难以直观呈现机械波中能量转换和能量传递的基本规律.本文从弹性介质最基本的胡克定律出发,从做功和能量转换的角度应用功能原理推导出了机械波的波动方程.本文提供了推导机械波波动方程的一种新方案,清晰地揭示了机械波中能量的转化和能量传递过程,有助于深入理解波动的物理本质.

Mechanical wave is the propagation of mechanical vibration in elastic medium,and it is a basic formation of matter motion.Most of the existing works of mechanical wave equation provide its derivation by using Newton's laws of motion.The derivation process makes it hard to intuitively present the basic laws of energy transformation and transmission in mechanical waves.This paper embarks from the famous Hooke's law of the elastic medium,and deduces the mechanical wave equation by applying the principle of power and energy from the perspective of energy transmissior.This paper provides a new scheme for deriving the wave equation of mechanical waves,and clearly reveals the process of energy transformation and energy transmission in mechanical waves,which is helpful to understand the physical process of waves deeply.