物理课程论文-基于C语言的驻波数据研究

1、基于c语言的驻波数据研究作者：学号（东南大学信息科学与工程学院，南京，211189）摘要：c语言是当前比较流行的一种编程语言，乂作为普通高等学校低年级的一门学习课程。在大学物理学中驻波-节的学 习过程中，笔者由此受到启发，决定利用这种计算机语言分析和研究骁波问题，从而把经典物理学课程融入到现代因索中， 使z变得更具实践性和数字化。关键词：驻波 c语言数字化(school of information science and engineeringsoutheast university, nanjing 211189)abstract: the c ianguage is currently

2、more popular as a programming ianguage, and it is also a low-grade learning programs in universities and colleges. when learn the stationary wave in the university physics , which inspired the author, i decided to use this computer ianguage analysis and research standing problem, thus bringing into

3、the modern classical physics curriculum factors, so that they are more practical and digital.key words: stationary wavec digital研究原理:研究表明:断某种运动是否具有波动的性的主要依据。t涉现象对于光学、声学和许多工程学科都非常重要，并 儿列波可以保持各自的特点（频率、波长、振且有广泛应用。幅、振动方向等）同时通过同一介质，好像在各自的传播过程中没冇遇到其他波一样。而在波相遇的机械波屮的驻波是一种特殊的干涉现像，它是区域，任一点的位移，为每个波单独存在时，在该通过在一

4、条直线上，利用相干波反向传播亞加，形点产生的位移的矢量和。这就是波的独立性和叠加成的一种分段振动现像。性原理。当几列波满足频率相同、振动方向相同、相遇 点有恒定相位差时，所产生的某些区域振动始终加x轴正方向和负方向传播。他们的表达式为:强，而另一些区域始终减弱的独特叠加现像就是波简化这一过程，我们设有两列简谐波，分别沿的干涉现像。干涉现象是波动所特有的现象，是判y2 = acos2( + -)利用三角关系，两列波壳加后的驻波方程:xy = yx + y2 = 2 a cos 2() cos 2ztfta此式就是驻波的波函数，即常称的驻波方程。x二i*h;yl二a*cos (w*t-k*x);y

5、2二a*cos (w*t+k*x);y二yl+y2;数字化实现：在用计算机c语言进行数字模拟时，我们収离散点坐标xj二ih,其中力为步长，则方程为xy. = 2 a cos 2兀(才)cos 2劝printf(t=%f x=%fyl二fy2=%fy=%fn", t, x, yl, y2, y);ji即为离散点兀的振动方程。整体显示各离散点 的必，就形成了某时刻t驻波波形。为简化起见， 取振幅a=a=lcm,波长a =lm,周期t=ls0用程序实现数据收集：#include<stdio. h>#include<math. h>void main()(float

6、x, t, h=0. 1, yl, y2, y;float a二0.01, w二2*3. 14159265, k;int i, j;krv;printfcw);for(j=0;j<=8;j+)t 二 0. 125*j;for(i=0;i<=20;i+)编译程序的数据图:d:microwft visual 5tu&omyprojects幽槪敦研郭 debug'曲迩孵兗 exe，旦旦 弓tto00000t电.000800t诩.丽i淋邛l 川卅川t屯側冏那tt 0 mb妣t f.nwni y.ucorut e.namt。血酗t诩.丽i淋邛tt屯側冏那t-0.125000t

7、 0.125000t=0.125000t 0.1250pat 0.125000it =0.1250pmx-0.200009 x=0.300080 x=0.400000 x-0.500000 x电6胡腑0 x=0.700b80 x.800b00 x=0.900080 x=l.000800 x=l.100009 x=l.200080 x=l.300000 x=l.400000 x-1.500000x=l.?00b80 x-1.800000 x=l.900080 x=2.000b80 x=0.080000 x=0.100080 x=9.200809 x=0.300000 x=0.400080x=0.

8、5b0000yl-0.003090 ji2.003090 y吨朋6180yl=-0.003090 0=-0.008090 yl-0.010000 yl=-0.008090 yl=-0.003090 yl-0.003090 yl=0.008090 yl=0.010000 yl-0.008090 yl=0.003090yl=-0.003090 yl=-0.008090 yl«-0.0100b0 yl=-0.008090 0=-0.003090yl-0.003090 yl=0.008099 yl=9.81 ms yl-fl.007071 yl=0.00987?y2=-0.083090 sl

9、2=-0.008090 1/2-0.010000 j/2-0.088090 y2tm3090 y2.003090 y2=fl.008090 jfi老.018800 y2电008盹 y2 电.083090y=-0.006180 y=-0.016180 jl-0.020000 y=-0.016180 y=-0.006180 y叩朋6180 y=0.016180 9=9.020000 9=0.016180 51=0.006180y2=-0.003的0 j/2-0.008090 y2-0.010b00 y2=-0.088090 sl2=-0.083090y2.00309o y2=«.0080

10、90 y2=e.010000 y2 =6.087871 y2 电.001564y=-8.006180 y=-0.016180 jj-0.020800 y=-0.016180y=-0.0061800.006180 y电.016180 y=0.020000 y=0.014142 y=0.011441yl=0.008910 j»2=-0.004540 y =0.004370 yl-0.004540 y2 -0.088910 y=-0.0043?0 yl-0.001564 y2=-0.0098?7 y=-0.011441yl=-0.00?0?ly2=-0.00?0?l尸弋.0141420.5

11、000000.5000000.5000000.500000x0.5000000.6250000625册00.6250000.6250000.625000乩625册006250册0.625000x0625册0x0.6250001.1000001.2000001.3000001.4000001.5000001.6000001.7000001.8000001.9000002.0000000.0000000.1000000.2000000.3000000.4000000.5000000.6000000.7000000.8000000.9000001.0000001.1000001.2000001.30

12、00001.400000yl=-0.008090 y2=-0.008090 ii=-0.016180 yl=-0.003090 y2=-0.003090 y=-0.006180 511=0.003090 yl=0.008090 yl=0.010000 111=0.008090 yl=0.003090 yl=-0.003090 yl=-0.008090 yl=-0.010000 jil=-8.00?8?l yl=-0.0098?7 yl=-0.008910 yl-0.004540 yl=0.001564 yl=0.00?0?l sil=0.0098? yl=0.008910 yl=0.00454

13、0 jil-0.001564 yl=-0.00?0?l jll-0.009877 yl=-0.008910 yl=-0.004540 虹咽0815641(2=0.003090 y2=0.008090 y2=0.010000 1)2=0.008090 y2=0.003090y=0.006180y=0.016180y=0.020000y=0.016180y=0.006180y2=-0.003090 yt鮒80ji2-0.008090 ji-0.016180 y2-0.010000 y-0.020000 y2=-0.00?0?l y-0.014142 y2=-0.001564 j/-8.811441

14、 y2=0.004540 y=-0.004370 ji2=0.008910 ji=0.0043?0 y2=0.0098?7 y=0.011441 y2=0.00?0?l y=0.014142 y2=8.m1564 y=0.011441 y2=-0.004540 y=0.004370 y2=-0.008910 y=-0.004370ji2-0.0098? ji-0.011441 y2=-0.00?0?l y-0.014142 j/2-0.001564 ji-0.011441 y2=0.004540 y-0.004370 y2=0.008910 y=0.0043702=0.0098? y=0.01

15、1441驻波不是行波。由图可知，两列相干波反向传t=0.875000 x=l.800000 yl=0.008910 y2=-0.004540 y=0.004370t=0.875000x=l.900000yl=0.00987?y2=0.9015640.011441t-0.875000x=2.000000yl=0.00?071y2=0.0070?lh.014142t=l.000090x=0.000000yl=0.010000y2=0.010080y=0.020000t=l 册丽00x羽.1朋眦yl=0.008090y2=0.008090y=0毗 6180t=l.000000x=0.200000yl

16、=0.003090y2=0.003090r0.006180t=1.800000x=0.300000yl=-0.003090y2=-0.003090i ji-0.0061801=1.000000x=0.400000yl-0.008090y2=-0.008090y=-0.016180t=l.000000x=0.509000yl=-0.01000by2=-0.010000i si-0.020080t=l.800000x=06俪0yl=-0.008090y2=-0.008090i jl-0.016180t=l.000000x=0.?00000yl=-0.003090y2=-0.003090i j/=-

17、0.006180t=l.000000x=0.800000yl=0.003090512=0.003090y=0.0061801=1.000000x=0.900000yl=0.008090y2=0.008090y=0.016180t=l.000000x=l.000800yl=0.010000ii2=0.010080y=0.020000t=l.800000x=l.100000yl=0.008090y2=0.008090y电血6188t=l.000000x=l.200000yl=0.003090y2=0.003090y=0.006180t=l.000000x=l.300800yl=-0.003090j

18、i2=-0.003090si=-0.006180e 俪90x=l.400000yl-0.008090y2=-0.0080901 ji-0.016180t=l.000000x=1.500000yl=-0.010000y2=-0.010000i j/=-0.0200b0t=l.800000x=l.600000yl=-0.008090y2=-0.008090ji=-0.016180t=l.000000x=l.700000jll =-0.083890y2=-0.003090y=-0.006180t=l.000090x=l.800000yl=0.003090ji2=0.003090y=0.006180t=l.800000x=l.900000yl=0.0080901/2=0