Exercise 11

波动

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题目 Investigate tne motion of a string for which one end is held fixed, while the other is made to oscillate. Do this by letting the srting element at one end move according to $y(i=0)=Asin(\omega t)$. You should find that this generates a wave that propagates toward the opposite end of the string. This wave is then reflected, and it interferes with the initial wave. Confirm that the frequencey of this wave equation. Also determine the values of $\omega$ that lead to standing waves.

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计算公式

$$r=c\Delta t/\Delta x$$ $$y(i,n+1)=2[1-r^2]y(i,n)-y(i,n-1)+r^2[y(i+1,n)+y(i-1,n)]$$ $$t_n=n\Delta t$$ $$y(i=0,n)=Asin(\omega t)$$ $$f=\omega /2pi$$ $$y(i=M,n)=0$$

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题解
在正弦波中，$r=0.5$并不能达到解，这时出现多个波叠加，不能直接使用。
$r$必须更加靠近1，才能使解的频谱变窄
(波长为30,r=0.5)
(波长为30,r=0.9979)
改变波长
(波长为100,r=0.9979)
驻波
(波长为50,运行时间分别为100和100+T/2)
本次作业与吴文雅同学合作完成，代码