CH15 Mechanical Waves
 

Mathematical description of traveling wave (行波)

 

Wave function (波函数): describes the position of any particle in the medium at any time
In positive x-direction:
               
In negative x-direction:
                
The above wave function satisfies the following one-dimensional wave equation
                
 
Mathematical description of a wave
sinusoidal wave moving in +x-direction
Wave number (波数):
Phase (相位):
 
Graphing wave functions
For wave moving in -x-direction
Phase velocity (相速度): speed of wave moving alongside a point of constant phase
 
Particle velocity and acceleration in a sinusoidal wave
 
Speed of a transverse wave
 
Energy in wave motion
Assuming:     
 
Wave intensity
For waves that travel in 3-D, the intensity is defined as the average power per unit area.?
Inverse-square law:
                              

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