黑管振动曲线研究高中物理教科书中关于“乐音由若干个振幅和频率不同的简谐振动合成的”知识，多年来由于没有先进的教学工具，以致于不容易说清楚，目前，可以借助于电脑的Excel进行研究，可以说明白了。人民教育出版社物理室编的全日制普通高级中学教科书（试验修订本必修）物理第一册第166页写道“黑管的振动是由9个频率不同的简谐振动合成的，乙图（本文图1）表示出了这9个简谐振动的频率和强度的关系”相对声强0400800120016002000频率图1为了研究黑管的振动曲线是怎样由这9个频率不同的简谐振动合成的，先看一看比较简单的情况。1．两个频率不同的简谐振动合成怎样的曲线？设y1=sinx,y2=sin2x,y=sinx+sin2x,令x从-6.3到6.3（单位：弧度）即从-2到2两个周期，每次梯增0.1。作出数据表及图象如下。xsinxsin2xsinx+sin2x-6.3-0.01681-0.03362-0.05044-6.20.0830890.1656040.248694-6.10.1821630.3582290.540392-60.2794150.5365730.815988-5.90.3738770.6935251.067402-5.80.4646020.8228291.287431-5.70.5506860.9193291.470014-5.60.6312670.9791781.610444-5.50.705540.999991.705531-5.40.7727640.9809361.753701-5.30.8322670.9227751.755043-5.20.8834550.8278261.711281-5.10.9258150.6998751.625689-50.9589240.5440211.502945-4.90.9824530.3664791.348932-4.80.9961650.1743271.170491-4.70.999923-0.024780.975148-4.60.993691-0.222890.770801-4.50.97753-0.412120.565412-4.40.951602-0.584920.3666851-4.30.916166-0.73440.181769-4.20.871576-0.85460.016977-4.10.818277-0.94073-0.12245-40.756802-0.98936-0.23256-3.90.687766-0.99854-0.31078-3.80.611858-0.96792-0.35606-3.70.529836-0.89871-0.36887-3.60.44252-0.79367-0.35115-3.50.350783-0.65699-0.3062-3.40.255541-0.49411-0.23857-3.30.157746-0.31154-0.1538-3.20.058374-0.11655-0.05818-3.1-0.041580.0830890.041509-3-0.141120.2794150.138295-2.9-0.239250.4646020.225353-2.8-0.334990.6312670.296278-2.7-0.427380.7727640.345385-2.6-0.51550.8834550.367953-2.5-0.598470.9589240.360452-2.4-0.675460.9961650.320701-2.3-0.745710.9936910.247986-2.2-0.80850.9516020.143106-2.1-0.863210.8715760.008366-2-0.90930.756802-0.15249-1.9-0.94630.611858-0.33444-1.8-0.973850.44252-0.53133-1.7-0.991660.255541-0.73612-1.6-0.999570.058374-0.9412-1.5-0.99749-0.14112-1.13861-1.4-0.98545-0.33499-1.32044-1.3-0.96356-0.5155-1.47906-1.2-0.93204-0.67546-1.6075-1.1-0.89121-0.8085-1.6997-1-0.84147-0.9093-1.75077-0.9-0.78333-0.97385-1.75717-0.8-0.71736-0.99957-1.71693-0.7-0.64422-0.98545-1.62967-0.6-0.56464-0.93204-1.49668-0.5-0.47943-0.84147-1.3209-0.4-0.38942-0.71736-1.10677-0.3-0.29552-0.56464-0.86016-0.2-0.19867-0.38942-0.58809-0.1-0.09983-0.19867-0.2985-2E-14-2E-14-3.9E-14-5.9E-1420.10.0998330.1986690.2985030.20.1986690.3894180.5880880.30.295520.5646420.8601630.40.3894180.7173561.1067740.50.4794260.8414711.3208970.60.5646420.9320391.4966820.70.6442180.985451.6296670.80.7173560.9995741.716930.90.7833270.9738481.75717510.8414710.9092971.7507681.10.8912070.8084961.6997041.20.9320390.6754631.6075021.30.9635580.5155011.479061.40.985450.3349881.3204381.50.9974950.141121.1386151.60.999574-0.058370.9411991.70.991665-0.255540.7361241.80.973848-0.442520.5313271.90.9463-0.611860.33444220.909297-0.75680.1524952.10.863209-0.87158-0.008372.20.808496-0.9516-0.143112.30.745705-0.99369-0.247992.40.675463-0.99616-0.32072.50.598472-0.95892-0.360452.60.515501-0.88345-0.367952.70.42738-0.77276-0.345382.80.334988-0.63127-0.296282.90.239249-0.4646-0.2253530.14112-0.27942-0.13833.10.041581-0.08309-0.041513.2-0.058370.1165490.0581753.3-0.157750.3115410.1537963.4-0.255540.4941130.2385723...
