题目内容
一列横波如图15所示,波长λ=8 m,实线表示t1=0时刻的波形图,虚线表示t2=0.005 s时刻的波形图.则:
(1)波速可能多大?
(2)若波沿x轴负方向传播且2T>t2-t1>T,波速又为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241405273068412.png)
(1)波速可能多大?
(2)若波沿x轴负方向传播且2T>t2-t1>T,波速又为多大?
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241405273068412.png)
(1) v=
=400(4n+3) m/s(n=0,1,2,…) (2) 2800 m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527353427.png)
(1)若波沿x轴正方向传播
t2-t1=
+nT,
得:T=
s
波速v=
=400(4n+1) m/s(n=0,1,2,…)
若波沿x轴负方向传播,t2-t1=
T+nT
得:T=
s
波速v=
=400(4n+3) m/s(n=0,1,2,…)
(2)若波沿x轴负方向传播
t2-t1=
+T, T=
s
所以速度v=
=2800 m/s
本题考查机械波的多解问题,因为该波传播方向未知,要分情况讨论,再有就是机械波的周期性决定了多解问题
t2-t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527399389.png)
得:T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527446611.png)
波速v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527353427.png)
若波沿x轴负方向传播,t2-t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527867385.png)
得:T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140528242647.png)
波速v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527353427.png)
(2)若波沿x轴负方向传播
t2-t1=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140528367473.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140528429484.png)
所以速度v=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824140527353427.png)
本题考查机械波的多解问题,因为该波传播方向未知,要分情况讨论,再有就是机械波的周期性决定了多解问题
![](http://thumb2018.1010pic.com/images/loading.gif)
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