题目内容
一列简谐横波在t=0时刻的波形如图中的实线所示,t=0.02s时刻
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247186246400.jpg)
的波形如图中虚线所示。若该波的周期T大于0.02s,则该波的传
播速度可能是
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241247186246400.jpg)
的波形如图中虚线所示。若该波的周期T大于0.02s,则该波的传
播速度可能是
A.2m/s |
B.3m/s |
C.4m/s |
D.5m/s |
B。
这类问题通常有两种解法。
解法一:质点振动法
(1)设波向右传播,则在0时刻
处的质点往上振动,
设经历
时间时质点运动到波峰的位置,则
,即
。
当
时,
,符合要求,此时
;
当
时,
,不符合要求。
(2)设波向左传播,则在0时刻
处的质点往下振动,
设经历
时间时质点运动到波峰的位置,则
,即
。
当
时,
,符合要求,此时
;
当
时,
,不符合要求。
综上所述,只有B选项正确。
解法二:波的平移法
(1)设波向右传播,只有当波传播的距离为
时,实线才会和虚线重合,即0时刻的波形才会演变成
时的波形,
,
所以
,
,
当
时,
,符合要求,此时
;
当
时,
,不符合要求。
(2)设波向左传播,只有当波传播的距离为
时,实线才会和虚线重合,即0时刻的波形才会演变成
时的波形,
,
所以
,
,
当
时,
,符合要求,此时
;
当
时,
,不符合要求。
综上所述,只有B选项正确。
解法一:质点振动法
(1)设波向右传播,则在0时刻
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718639247.gif)
设经历
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718655204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718671544.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718686712.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718702243.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718717442.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718733714.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749232.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749454.gif)
(2)设波向左传播,则在0时刻
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718639247.gif)
设经历
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718655204.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718795546.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718811708.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718702243.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718842639.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718858768.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749232.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718889530.gif)
综上所述,只有B选项正确。
解法二:波的平移法
(1)设波向右传播,只有当波传播的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718920554.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718936264.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718936330.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718951874.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718967617.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718702243.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718717442.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124719014480.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749232.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749454.gif)
(2)设波向左传播,只有当波传播的距离为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124719061558.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718936264.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718936330.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124719092886.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124719107631.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718702243.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718842639.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124719466482.gif)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718749232.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824124718889530.gif)
综上所述,只有B选项正确。
![](http://thumb2018.1010pic.com/images/loading.gif)
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