8 15-3 The wave equation of plane harmonic waves 1. The plane harmonic wavey If the motion of the wave wave source source and the particles in the medium are harmonic motion(vibration), this kind t(s) of wave is known harmonic wave y=Acos( at+P) Note: here y is the displacement of particles at wave source and in the medium
The wave equation of plane harmonic waves 1. The plane harmonic wave If the motion of the wave source and the particles in the medium are harmonic motion(vibration), this kind of wave is known harmonic wave: y A cos( t ) Note: here y is the displacement of particles at wave source and in the medium. t(s) y o wave source
If the wave front of the harmonic wave is plane, this wave is called as the plane harmonic Point p wave。 波面 波 A 平面波 ■■■口■■■■■口■■■■圆 The motion of any point e Choose one wave in this plane is as same as Eline to study the: that of point p e wave motion such aasX-axis
平面波 波 线 波面 球面波 P x A A A If the wave front of the harmonic wave is plane, this wave is called as the plane harmonic wave. The motion of any point in this plane is as same as that of point P. Choose one wave line to study the wave motion such as x-axis. y o Point P t
2. The wave equation of plane harmonic wave(介绍) 在波线0x上任选 点P来研究.已知o点 的运动方程为 ■■■■■■■ yo= A cos( at+o) P点的运动状态是由o点的运动状态经一段时间传过来 的
2. The wave equation of plane harmonic wave（介绍） 在波线ox上任选一 点P来研究. 已知 o点 的运动方程为 y A cos( t ) o P点的运动状态是由o点的运动状态经一段时间传过来 的。 y o x P x V x t P V
△t ■■■■■■ P X ■■■■ 经时间达 -M时刻o点 t时刻P点的运动 的运动状态 写相筒…犬态
t时刻P点的运动 状态 时刻o点 的运动状态 V x t P 与相同 经 V 时间达 x P y o x P x V x t P V
经时间达 -P时刻P点 时刻P点的运动 的运动状态 写与相同 状态 ■■ ■■■■口 t时刻P点的运动 yQ(t=)=Aco(-2)+]=状态 所以t时刻P点的运动状态为: yp(t=y, (t- P)=acoso(t -P )+ol 因为P为任意一点,去掉下标P,x轴上任一点(坐标x) 满足: y=Acos@(t-=)+o
t时刻P点的运动 状态 时刻P点 的运动状态 V x t P 与相同 经 V 时间达 x P ( ) cos[( ) ] V x A t V x y t P P o = t时刻P点的运动 状态 所以t时刻P点的运动状态为： ( ) ( ) cos[( ) ] V x A t V x y t y t P P P o 因为P为任意一点，去掉下标P, x轴上任一点(坐标x） 满足：