题目内容
图中实线是一列简谐波在某一时刻的波形图线,虚线是0.2s后它的波形图线。这列波可能的传播速度是_______。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521356493146.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521356493146.png)
(20n+5)m/s和(20m+15)m/s,(n=0,1,2,…)
【错解分析】错解:从图上可以看出波长λ=4m,而从两次的波形图可知:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152135727702.png)
所以T=0.8s
由波速公式:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152135805519.png)
代入数据v=5m/s.
(1)在没有分析出此波的传播方向前,就认定
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152135899628.png)
(2)没有考虑到波的传播过程的周期性。也就是说,不仅
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136008421.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136195443.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136257494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136008421.png)
【正解】从图上可以看出λ=4m。
当波沿x正方向传播时,两次波形之间间隔的时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136008421.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136195443.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136257494.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136850584.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152136975793.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152137147817.png)
由波速公式:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152135805519.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521374121245.png)
当波沿x正方向传播时,两次波形之间间隔的时间为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152137661484.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152137755514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152137880534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152137958632.png)
而
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152138114821.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152138270855.png)
由波速公式:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824152135805519.png)
解得:
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241521386131322.png)
此题的答案为:(20n+5)m/s和(20m+15)m/s,(n=0,1,2,…)
【点评】对于这种已知条件较为含糊的波的问题,要从波的传播方向、时间和空间的周期性等方面进行全面周到的分析,这也是解决机械波问题时,初学者经常忽略的问题。
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目