题目内容
图是某时刻一列横波在空间传播的波形图线。已知波是沿x轴正方向传播,波速为4m/s,试计算并画出经过此时之后1.25s的空间波形图。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521394241400.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521394241400.png)
见解析
【错解分析】错解一:由图可以看出,波长
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152139611578.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152139736523.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152139814628.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521398926370.png)
错解二:波长
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521400171102.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140079391.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521401425664.png)
错解三:由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140204975.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140313713.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521404075816.png)
错解一、错解二没有重视单位的一致性,在此题中波长从图中只能得出λ=8cm,而波速给出的却是国际单位4m/s。因此,求周期时,应先将波长的单位统一到国际单位制上来。
错解三虽然计算对了,但是,在波向前(沿x轴正方向)传播了62.5个波长时的波形,应是在原来的波形基础上向x正方扩展62.5个波长。
【正解】由波形图已知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140516629.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140204975.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140313713.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152140719338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521407976624.png)
再将此图向前扩展62个波长即为题目要求,波形如图。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521408595348.png)
【点评】波形图反映了波在传播过程中某时刻在波的传播方向上各质点离开平衡位置的位移情况,由于波只能以有限的速度向前传播,所以离振源远的质点总要滞后一段时间,滞后的时间与传播的距离成正比,即滞后一个周期。两个质点之间的平衡位置距离就是一个波长,经过多少个周期,波就向前传播了多少个波长,而振源就做了多少次全振动,这就是此类问题的关键所在。
![](http://thumb2018.1010pic.com/images/loading.gif)
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