题目内容
一列简谐波在传播方向上相距x="3" m的两质点P、Q的振动图象如图12-3-11所示.这列波的波长可能是( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241205368162395.jpg)
图12-3-11
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241205368162395.jpg)
图12-3-11
A.4 m | B.8 m | C.12 m | D.16 m |
AC
由于P、Q两点离波源的远、近不明确,因此要分两种情况讨论.
(1)若P比Q离波源近,则P先振动.比较t=0时两质点的位移可知,Q比P落后的时间为
Δt=
T+nT,(n=0,1,2,…)
则x=vΔt=
Δt=
(
T+nT)=(
+n)λ,(n=0,1,2,…)
得λ=
=
m,(n=0,1,2,…)
当n=0时,λ=" 4" m;
当n=1时,λ=
m.
随着n取值的增大,波长λ变短.这种情况下最大波长为λ="4" m.
(2)若Q比P离波源近,则Q先振动,同样由比较t=0时,两质点的位移可知,P比Q落后的时间为
Δt=
T+nT,(n=0,1,2,…)
则x=
Δt=
(
T+nT)=(
+n)λ,(n="0,1,2," …)
得λ=
m,(n=0,1,2,…)
当n=0时,λ="12" m;
当n=1时,λ=
m;
当n=2时,λ=
m.
(1)若P比Q离波源近,则P先振动.比较t=0时两质点的位移可知,Q比P落后的时间为
Δt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536832223.gif)
则x=vΔt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536879234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536879234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536832223.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536832223.gif)
得λ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536957423.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536972438.gif)
当n=0时,λ=" 4" m;
当n=1时,λ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536972245.gif)
随着n取值的增大,波长λ变短.这种情况下最大波长为λ="4" m.
(2)若Q比P离波源近,则Q先振动,同样由比较t=0时,两质点的位移可知,P比Q落后的时间为
Δt=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537003221.gif)
则x=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536879234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120536879234.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537003221.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537003221.gif)
得λ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537081438.gif)
当n=0时,λ="12" m;
当n=1时,λ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537331246.gif)
当n=2时,λ=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824120537347224.gif)
![](http://thumb2018.1010pic.com/images/loading.gif)
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