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1、用心爱心专心1 无线电调幅图象研究 高中物理教科书在 “电磁场和电磁波”一章“无线电波的发射和 接收”一节中，有关无线电调幅的知识有“在电磁波发射技术中，使 电磁波随各种信号而改变叫调制。 使高频震荡的振幅随信号而改变叫 做调幅，调幅广播（ AM ）一般使用中波和短波波段。 ”的内容。（见 人民教育出版社物理室编著全日制普通中学教科书（必修加选修） 物理第二册第 245 页） 。 以前，对这个内容不容易说清楚，现在，可以借助电子计算机的 Exel 把它讲明白。 1等幅高频振荡 实际的高频振荡（例如中波段）为535-1605kHz，短波段的 频率更高。频率太高，在图象中看不出来，为说明问题，我们
2、把 三角函数设为y=sin16x，以区别于声音信号（低频信号） 。而声 音信号设为 y=sin2x。 在-到 2的范围内设定自变量x, 为求图象的清晰，间隔 设为 0.01，求出对应的 y=sin16x 的值，在求值过程中注意把x 的数值转化为弧度。表1 和图 1 分别为数据表和图象。 xcos16x -11 -0.990.876307 -0.980.535827 -0.970.062791 -0.96-0.42578 -0.95-0.80902 -0.94-0.99211 -0.93-0.92978 -0.92-0.63742 用心爱心专心2 -0.91-0.18738 -0.90.3090
3、17 -0.890.728969 -0.880.968583 -0.870.968583 -0.860.728969 -0.850.309017 -0.84-0.18738 -0.83-0.63742 -0.82-0.92978 -0.81-0.99211 -0.8-0.80902 -0.79-0.42578 -0.780.062791 -0.770.535827 -0.760.876307 -0.751 -0.740.876307 -0.730.535827 -0.720.062791 -0.71-0.42578 -0.7-0.80902 -0.69-0.99211 -0.68-0.9297
4、8 -0.67-0.63742 -0.66-0.18738 -0.650.309017 -0.640.728969 -0.630.968583 -0.620.968583 -0.610.728969 -0.60.309017 -0.59-0.18738 -0.58-0.63742 -0.57-0.92978 -0.56-0.99211 -0.55-0.80902 -0.54-0.42578 -0.530.062791 -0.520.535827 -0.510.876307 -0.51 -0.490.876307 -0.480.535827 用心爱心专心3 -0.470.062791 -0.46
5、-0.42578 -0.45-0.80902 -0.44-0.99211 -0.43-0.92978 -0.42-0.63742 -0.41-0.18738 -0.40.309017 -0.390.728969 -0.380.968583 -0.370.968583 -0.360.728969 -0.350.309017 -0.34-0.18738 -0.33-0.63742 -0.32-0.92978 -0.31-0.99211 -0.3-0.80902 -0.29-0.42578 -0.280.062791 -0.270.535827 -0.260.876307 -0.251 -0.240
6、.876307 -0.230.535827 -0.220.062791 -0.21-0.42578 -0.2-0.80902 -0.19-0.99211 -0.18-0.92978 -0.17-0.63742 -0.16-0.18738 -0.150.309017 -0.140.728969 -0.130.968583 -0.120.968583 -0.110.728969 -0.10.309017 -0.09-0.18738 -0.08-0.63742 -0.07-0.92978 -0.06-0.99211 -0.05-0.80902 -0.04-0.42578 用心爱心专心4 -0.030
7、.062791 -0.020.535827 -0.010.876307 01 0.010.876307 0.020.535827 0.030.062791 0.04-0.42578 0.05-0.80902 0.06-0.99211 0.07-0.92978 0.08-0.63742 0.09-0.18738 0.10.309017 0.110.728969 0.120.968583 0.130.968583 0.140.728969 0.150.309017 0.16-0.18738 0.17-0.63742 0.18-0.92978 0.19-0.99211 0.2-0.80902 0.2
8、1-0.42578 0.220.062791 0.230.535827 0.240.876307 0.251 0.260.876307 0.270.535827 0.280.062791 0.29-0.42578 0.3-0.80902 0.31-0.99211 0.32-0.92978 0.33-0.63742 0.34-0.18738 0.350.309017 0.360.728969 0.370.968583 0.380.968583 0.390.728969 0.40.309017 用心爱心专心5 0.41-0.18738 0.42-0.63742 0.43-0.92978 0.44-
9、0.99211 0.45-0.80902 0.46-0.42578 0.470.062791 0.480.535827 0.490.876307 0.51 0.510.876307 0.520.535827 0.530.062791 0.54-0.42578 0.55-0.80902 0.56-0.99211 0.57-0.92978 0.58-0.63742 0.59-0.18738 0.60.309017 0.610.728969 0.620.968583 0.630.968583 0.640.728969 0.650.309017 0.66-0.18738 0.67-0.63742 0.
10、68-0.92978 0.69-0.99211 0.7-0.80902 0.71-0.42578 0.720.062791 0.730.535827 0.740.876307 0.751 0.760.876307 0.770.535827 0.780.062791 0.79-0.42578 0.8-0.80902 0.81-0.99211 0.82-0.92978 0.83-0.63742 0.84-0.18738 用心爱心专心6 0.850.309017 0.860.728969 0.870.968583 0.880.968583 0.890.728969 0.90.309017 0.91-
11、0.18738 0.92-0.63742 0.93-0.92978 0.94-0.99211 0.95-0.80902 0.96-0.42578 0.970.062791 0.980.535827 0.990.876307 11 1.010.876307 1.020.535827 1.030.062791 1.04-0.42578 1.05-0.80902 1.06-0.99211 1.07-0.92978 1.08-0.63742 1.09-0.18738 1.10.309017 1.110.728969 1.120.968583 1.130.968583 1.140.728969 1.15
12、0.309017 1.16-0.18738 1.17-0.63742 1.18-0.92978 1.19-0.99211 1.2-0.80902 1.21-0.42578 1.220.062791 1.230.535827 1.240.876307 1.251 1.260.876307 1.270.535827 1.280.062791 用心爱心专心7 1.29-0.42578 1.3-0.80902 1.31-0.99211 1.32-0.92978 1.33-0.63742 1.34-0.18738 1.350.309017 1.360.728969 1.370.968583 1.380.
13、968583 1.390.728969 1.40.309017 1.41-0.18738 1.42-0.63742 1.43-0.92978 1.44-0.99211 1.45-0.80902 1.46-0.42578 1.470.062791 1.480.535827 1.490.876307 1.51 表 1 x 与 cos16x数据表 cos16x -1.5 -1 -0.5 0 0.5 1 1.5 050100150200250300 cos16x 图 1 y=cos16x图象 2低频声音信号 在-到 2的范围内设定自变量x,，间隔同样设为0.01，求出 对应的 y=sin2x 的值，然
14、后画出图象。表2 和图 2 分别为数据表 用心爱心专心8 和图象。 x cos2x -11 -0.990.998027 -0.980.992115 -0.970.982287 -0.960.968583 -0.950.951057 -0.940.929776 -0.930.904827 -0.920.876307 -0.910.844328 -0.90.809017 -0.890.770513 -0.880.728969 -0.870.684547 -0.860.637424 -0.850.587785 -0.840.535827 -0.830.481754 -0.820.425779 -0.
15、810.368125 -0.80.309017 -0.790.24869 -0.780.187381 -0.770.125333 -0.760.062791 -0.75-1.8E-16 -0.74-0.06279 -0.73-0.12533 -0.72-0.18738 -0.71-0.24869 -0.7-0.30902 -0.69-0.36812 -0.68-0.42578 -0.67-0.48175 -0.66-0.53583 -0.65-0.58779 -0.64-0.63742 -0.63-0.68455 -0.62-0.72897 -0.61-0.77051 用心爱心专心9 -0.6
16、-0.80902 -0.59-0.84433 -0.58-0.87631 -0.57-0.90483 -0.56-0.92978 -0.55-0.95106 -0.54-0.96858 -0.53-0.98229 -0.52-0.99211 -0.51-0.99803 -0.5-1 -0.49-0.99803 -0.48-0.99211 -0.47-0.98229 -0.46-0.96858 -0.45-0.95106 -0.44-0.92978 -0.43-0.90483 -0.42-0.87631 -0.41-0.84433 -0.4-0.80902 -0.39-0.77051 -0.38
17、-0.72897 -0.37-0.68455 -0.36-0.63742 -0.35-0.58779 -0.34-0.53583 -0.33-0.48175 -0.32-0.42578 -0.31-0.36812 -0.3-0.30902 -0.29-0.24869 -0.28-0.18738 -0.27-0.12533 -0.26-0.06279 -0.256.28E-15 -0.240.062791 -0.230.125333 -0.220.187381 -0.210.24869 -0.20.309017 -0.190.368125 -0.180.425779 -0.170.481754
18、用心爱心专心10 -0.160.535827 -0.150.587785 -0.140.637424 -0.130.684547 -0.120.728969 -0.110.770513 -0.10.809017 -0.090.844328 -0.080.876307 -0.070.904827 -0.060.929776 -0.050.951057 -0.040.968583 -0.030.982287 -0.020.992115 -0.010.998027 01 0.010.998027 0.020.992115 0.030.982287 0.040.968583 0.050.951057
19、0.060.929776 0.070.904827 0.080.876307 0.090.844328 0.10.809017 0.110.770513 0.120.728969 0.130.684547 0.140.637424 0.150.587785 0.160.535827 0.170.481754 0.180.425779 0.190.368125 0.20.309017 0.210.24869 0.220.187381 0.230.125333 0.240.062791 0.256.13E-17 0.26-0.06279 0.27-0.12533 用心爱心专心11 0.28-0.1
20、8738 0.29-0.24869 0.3-0.30902 0.31-0.36812 0.32-0.42578 0.33-0.48175 0.34-0.53583 0.35-0.58779 0.36-0.63742 0.37-0.68455 0.38-0.72897 0.39-0.77051 0.4-0.80902 0.41-0.84433 0.42-0.87631 0.43-0.90483 0.44-0.92978 0.45-0.95106 0.46-0.96858 0.47-0.98229 0.48-0.99211 0.49-0.99803 0.5-1 0.51-0.99803 0.52-
21、0.99211 0.53-0.98229 0.54-0.96858 0.55-0.95106 0.56-0.92978 0.57-0.90483 0.58-0.87631 0.59-0.84433 0.6-0.80902 0.61-0.77051 0.62-0.72897 0.63-0.68455 0.64-0.63742 0.65-0.58779 0.66-0.53583 0.67-0.48175 0.68-0.42578 0.69-0.36812 0.7-0.30902 0.71-0.24869 用心爱心专心12 0.72-0.18738 0.73-0.12533 0.74-0.06279
22、 0.75-1.8E-16 0.760.062791 0.770.125333 0.780.187381 0.790.24869 0.80.309017 0.810.368125 0.820.425779 0.830.481754 0.840.535827 0.850.587785 0.860.637424 0.870.684547 0.880.728969 0.890.770513 0.90.809017 0.910.844328 0.920.876307 0.930.904827 0.940.929776 0.950.951057 0.960.968583 0.970.982287 0.9
23、80.992115 0.990.998027 11 1.010.998027 1.020.992115 1.030.982287 1.040.968583 1.050.951057 1.060.929776 1.070.904827 1.080.876307 1.090.844328 1.10.809017 1.110.770513 1.120.728969 1.130.684547 1.140.637424 1.150.587785 用心爱心专心13 1.160.535827 1.170.481754 1.180.425779 1.190.368125 1.20.309017 1.210.2
24、4869 1.220.187381 1.230.125333 1.240.062791 1.253.06E-16 1.26-0.06279 1.27-0.12533 1.28-0.18738 1.29-0.24869 1.3-0.30902 1.31-0.36812 1.32-0.42578 1.33-0.48175 1.34-0.53583 1.35-0.58779 1.36-0.63742 1.37-0.68455 1.38-0.72897 1.39-0.77051 1.4-0.80902 1.41-0.84433 1.42-0.87631 1.43-0.90483 1.44-0.9297
25、8 1.45-0.95106 1.46-0.96858 1.47-0.98229 1.48-0.99211 1.49-0.99803 1.5-1 用心爱心专心14 -1.5 -1 -0.5 0 0.5 1 1.5 -2-1012 系列1 图 2 y=cos2x的图象 3调幅 用心爱心专心15 在同一幅图中画出y1=cos2x, y2=-cos2x, y3=cos2x cos16x的图象， 用心爱心专心16 数据表和图象分别如表3 和图 3 所示。 xcos2x“-cos2x“cos2xcos16x -11-11 -0.990.998027-0.998030.874577 -0.980.9921
26、15-0.992110.531602 -0.970.982287-0.982290.061678 -0.960.968583-0.96858-0.4124 -0.950.951057-0.95106-0.76942 -0.940.929776-0.92978-0.92244 -0.930.904827-0.90483-0.84129 -0.920.876307-0.87631-0.55858 -0.910.844328-0.84433-0.15821 -0.90.809017-0.809020.25 -0.890.770513-0.770510.56168 -0.880.728969-0.72
27、8970.706067 -0.870.684547-0.684550.663041 -0.860.637424-0.637420.464662 -0.850.587785-0.587790.181636 -0.840.535827-0.53583-0.1004 -0.830.481754-0.48175-0.30708 -0.820.425779-0.42578-0.39588 -0.810.368125-0.36812-0.36522 -0.80.309017-0.30902-0.25 -0.790.24869-0.24869-0.10589 -0.780.187381-0.187380.0
28、11766 -0.770.125333-0.125330.067157 -0.760.062791-0.062790.055024 -0.75-1.8E-161.84E-16-1.8E-16 -0.74-0.062790.062791-0.05502 -0.73-0.125330.125333-0.06716 -0.72-0.187380.187381-0.01177 -0.71-0.248690.248690.105887 -0.7-0.309020.3090170.25 -0.69-0.368120.3681250.365222 -0.68-0.425780.4257790.39588 -
29、0.67-0.481750.4817540.307081 -0.66-0.535830.5358270.100404 -0.65-0.587790.587785-0.18164 -0.64-0.637420.637424-0.46466 -0.63-0.684550.684547-0.66304 -0.62-0.728970.728969-0.70607 -0.61-0.770510.770513-0.56168 -0.6-0.809020.809017-0.25 用心爱心专心17 -0.59-0.844330.8443280.158211 -0.58-0.876310.8763070.558
30、579 -0.57-0.904830.9048270.841287 -0.56-0.929780.9297760.922445 -0.55-0.951060.9510570.769421 -0.54-0.968580.9685830.412403 -0.53-0.982290.982287-0.06168 -0.52-0.992110.992115-0.5316 -0.51-0.998030.998027-0.87458 -0.5-11-1 -0.49-0.998030.998027-0.87458 -0.48-0.992110.992115-0.5316 -0.47-0.982290.982
31、287-0.06168 -0.46-0.968580.9685830.412403 -0.45-0.951060.9510570.769421 -0.44-0.929780.9297760.922445 -0.43-0.904830.9048270.841287 -0.42-0.876310.8763070.558579 -0.41-0.844330.8443280.158211 -0.4-0.809020.809017-0.25 -0.39-0.770510.770513-0.56168 -0.38-0.728970.728969-0.70607 -0.37-0.684550.684547-
32、0.66304 -0.36-0.637420.637424-0.46466 -0.35-0.587790.587785-0.18164 -0.34-0.535830.5358270.100404 -0.33-0.481750.4817540.307081 -0.32-0.425780.4257790.39588 -0.31-0.368120.3681250.365222 -0.3-0.309020.3090170.25 -0.29-0.248690.248690.105887 -0.28-0.187380.187381-0.01177 -0.27-0.125330.125333-0.06716
33、 -0.26-0.062790.062791-0.05502 -0.256.28E-15-6.3E-156.28E-15 -0.240.062791-0.062790.055024 -0.230.125333-0.125330.067157 -0.220.187381-0.187380.011766 -0.210.24869-0.24869-0.10589 -0.20.309017-0.30902-0.25 -0.190.368125-0.36812-0.36522 -0.180.425779-0.42578-0.39588 -0.170.481754-0.48175-0.30708 -0.1
34、60.535827-0.53583-0.1004 用心爱心专心18 -0.150.587785-0.587790.181636 -0.140.637424-0.637420.464662 -0.130.684547-0.684550.663041 -0.120.728969-0.728970.706067 -0.110.770513-0.770510.56168 -0.10.809017-0.809020.25 -0.090.844328-0.84433-0.15821 -0.080.876307-0.87631-0.55858 -0.070.904827-0.90483-0.84129 -0
35、.060.929776-0.92978-0.92244 -0.050.951057-0.95106-0.76942 -0.040.968583-0.96858-0.4124 -0.030.982287-0.982290.061678 -0.020.992115-0.992110.531602 -0.010.998027-0.998030.874577 01-11 0.010.998027-0.998030.874577 0.020.992115-0.992110.531602 0.030.982287-0.982290.061678 0.040.968583-0.96858-0.4124 0.
36、050.951057-0.95106-0.76942 0.060.929776-0.92978-0.92244 0.070.904827-0.90483-0.84129 0.080.876307-0.87631-0.55858 0.090.844328-0.84433-0.15821 0.10.809017-0.809020.25 0.110.770513-0.770510.56168 0.120.728969-0.728970.706067 0.130.684547-0.684550.663041 0.140.637424-0.637420.464662 0.150.587785-0.587
37、790.181636 0.160.535827-0.53583-0.1004 0.170.481754-0.48175-0.30708 0.180.425779-0.42578-0.39588 0.190.368125-0.36812-0.36522 0.20.309017-0.30902-0.25 0.210.24869-0.24869-0.10589 0.220.187381-0.187380.011766 0.230.125333-0.125330.067157 0.240.062791-0.062790.055024 0.256.13E-17-6.1E-176.13E-17 0.26-
38、0.062790.062791-0.05502 0.27-0.125330.125333-0.06716 0.28-0.187380.187381-0.01177 用心爱心专心19 0.29-0.248690.248690.105887 0.3-0.309020.3090170.25 0.31-0.368120.3681250.365222 0.32-0.425780.4257790.39588 0.33-0.481750.4817540.307081 0.34-0.535830.5358270.100404 0.35-0.587790.587785-0.18164 0.36-0.637420
39、.637424-0.46466 0.37-0.684550.684547-0.66304 0.38-0.728970.728969-0.70607 0.39-0.770510.770513-0.56168 0.4-0.809020.809017-0.25 0.41-0.844330.8443280.158211 0.42-0.876310.8763070.558579 0.43-0.904830.9048270.841287 0.44-0.929780.9297760.922445 0.45-0.951060.9510570.769421 0.46-0.968580.9685830.41240
40、3 0.47-0.982290.982287-0.06168 0.48-0.992110.992115-0.5316 0.49-0.998030.998027-0.87458 0.5-11-1 0.51-0.998030.998027-0.87458 0.52-0.992110.992115-0.5316 0.53-0.982290.982287-0.06168 0.54-0.968580.9685830.412403 0.55-0.951060.9510570.769421 0.56-0.929780.9297760.922445 0.57-0.904830.9048270.841287 0
41、.58-0.876310.8763070.558579 0.59-0.844330.8443280.158211 0.6-0.809020.809017-0.25 0.61-0.770510.770513-0.56168 0.62-0.728970.728969-0.70607 0.63-0.684550.684547-0.66304 0.64-0.637420.637424-0.46466 0.65-0.587790.587785-0.18164 0.66-0.535830.5358270.100404 0.67-0.481750.4817540.307081 0.68-0.425780.4
42、257790.39588 0.69-0.368120.3681250.365222 0.7-0.309020.3090170.25 0.71-0.248690.248690.105887 0.72-0.187380.187381-0.01177 用心爱心专心20 0.73-0.125330.125333-0.06716 0.74-0.062790.062791-0.05502 0.75-1.8E-161.84E-16-1.8E-16 0.760.062791-0.062790.055024 0.770.125333-0.125330.067157 0.780.187381-0.187380.0
43、11766 0.790.24869-0.24869-0.10589 0.80.309017-0.30902-0.25 0.810.368125-0.36812-0.36522 0.820.425779-0.42578-0.39588 0.830.481754-0.48175-0.30708 0.840.535827-0.53583-0.1004 0.850.587785-0.587790.181636 0.860.637424-0.637420.464662 0.870.684547-0.684550.663041 0.880.728969-0.728970.706067 0.890.7705
44、13-0.770510.56168 0.90.809017-0.809020.25 0.910.844328-0.84433-0.15821 0.920.876307-0.87631-0.55858 0.930.904827-0.90483-0.84129 0.940.929776-0.92978-0.92244 0.950.951057-0.95106-0.76942 0.960.968583-0.96858-0.4124 0.970.982287-0.982290.061678 0.980.992115-0.992110.531602 0.990.998027-0.998030.87457
45、7 11-11 1.010.998027-0.998030.874577 1.020.992115-0.992110.531602 1.030.982287-0.982290.061678 1.040.968583-0.96858-0.4124 1.050.951057-0.95106-0.76942 1.060.929776-0.92978-0.92244 1.070.904827-0.90483-0.84129 1.080.876307-0.87631-0.55858 1.090.844328-0.84433-0.15821 1.10.809017-0.809020.25 1.110.77
46、0513-0.770510.56168 1.120.728969-0.728970.706067 1.130.684547-0.684550.663041 1.140.637424-0.637420.464662 1.150.587785-0.587790.181636 1.160.535827-0.53583-0.1004 用心爱心专心21 1.170.481754-0.48175-0.30708 1.180.425779-0.42578-0.39588 1.190.368125-0.36812-0.36522 1.20.309017-0.30902-0.25 1.210.24869-0.2
47、4869-0.10589 1.220.187381-0.187380.011766 1.230.125333-0.125330.067157 1.240.062791-0.062790.055024 1.253.06E-16-3.1E-163.06E-16 1.26-0.062790.062791-0.05502 1.27-0.125330.125333-0.06716 1.28-0.187380.187381-0.01177 1.29-0.248690.248690.105887 1.3-0.309020.3090170.25 1.31-0.368120.3681250.365222 1.3
48、2-0.425780.4257790.39588 1.33-0.481750.4817540.307081 1.34-0.535830.5358270.100404 1.35-0.587790.587785-0.18164 1.36-0.637420.637424-0.46466 1.37-0.684550.684547-0.66304 1.38-0.728970.728969-0.70607 1.39-0.770510.770513-0.56168 1.4-0.809020.809017-0.25 1.41-0.844330.8443280.158211 1.42-0.876310.8763
49、070.558579 1.43-0.904830.9048270.841287 1.44-0.929780.9297760.922445 1.45-0.951060.9510570.769421 1.46-0.968580.9685830.412403 1.47-0.982290.982287-0.06168 1.48-0.992110.992115-0.5316 1.49-0.998030.998027-0.87458 1.5-11-1 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5-1-0.500.511.52 系列1 系列2 系列3 用心爱心专心22 图 3 调幅示意图。 从图 3 可以看出，高频震荡的振幅确实随声音信号的变化而变化 了，这就是调幅。此处无声胜有声，通过图象，清楚地说明了调幅的 原理与过程，是过去千言万语讲不明白的。 要注意，这不是死的图象， 要在课堂上展示成象的过程。