振动
一、振动方程:\(y=Acos(\omega t+\varphi)\)
(\(\omega =2\pi \nu=\frac{2\pi}{T}\) )
二、波动方程:\(y(x,t)=Acos(2\pi\nu t+\varphi-\frac{2\pi(x-x_0)}{\lambda})\)=\(Acos(2\pi\nu t+\varphi-\frac{\omega(x-x_0)}{\mu})\)
(波向x正方向传播则\(\varphi\)后是负号,否则是正号);
三、反射波:
假设入射波为:\(y(x,t)=Acos(2\pi\nu t+\varphi-\frac{2\pi x}{\lambda})\),则
\(y'(x,t)=\left\{\begin{array}
固定端反射:y(x,t)=Acos(2\pi\nu t+\varphi+\frac{2\pi x}{\lambda}+\pi),有半波损失 \\
自由端反射:y(x,t)=Acos(2\pi\nu t+\varphi+\frac{2\pi x}{\lambda}),无半波损失
\end{array} \right.\)
四、驻波:\(y=y_1+y_2=2Acos(\frac{2\pi x}{\lambda}+\frac{\varphi_2-\varphi_1}{2})cos(2\pi\nu t+\frac{\varphi_2+\varphi_1}{2})\)
(注意式中的\(\varphi_2-\varphi_1\)是向x轴负方向的波-向x轴正方向的波)
波节:\(cos(\frac{2\pi x}{\lambda}+\frac{\varphi_2-\varphi_1}{2})=0\)处,动能为0;
波腹:\(cos(\frac{2\pi x}{\lambda}+\frac{\varphi_2-\varphi_1}{2})=1\)处,振动势能为0;
五、光的干涉:
干涉条件:
1)频率相同 2)振动方向平行 3)相位差恒定
光程差:
相位差:\(\Delta\varphi=\frac{2\pi r_2}{\lambda_2}-\frac{2\pi r_1}{\lambda_1}+\varphi_1-\varphi_2\)
又有\(\lambda_1=\frac{\lambda}{n_1},\lambda_2=\frac{\lambda}{n_2}\)
所以\(\Delta\varphi=2\pi(\frac{n_2 r_2}{\lambda}-\frac{n_1 r_1}{\lambda})\)
则光程差\(\epsilon=n_2 r_2-n_1 r_1)\)
光程差与相位差的关系是\(\Delta\varphi=\frac{2\pi}{\lambda} \epsilon\)
fff