题目内容
一列横波在x轴上传播,如图所示的实线和虚线为这列波在t1 = 0s和t2 =0.075s时的波形。
(1)若波速为400 m/s,求周期及波传播的方向。
(2)若波向右传播且(t2 —t1) 小于周期,求t1 = 0s时位于x ="4" m处的质点P的振动方向及波传播的速度大小。![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218171309991.jpg)
(1)若波速为400 m/s,求周期及波传播的方向。
(2)若波向右传播且(t2 —t1) 小于周期,求t1 = 0s时位于x ="4" m处的质点P的振动方向及波传播的速度大小。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408241218171309991.jpg)
(1)T =0.02s,波的传播方向沿
轴的负方向。
(2)质点的振动方向沿y轴正方向;
=26.7m/s
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817146187.gif)
(2)质点的振动方向沿y轴正方向;
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817162193.gif)
由图知
=8m (1分)
(1)若v=400m/s
则:周期T=
=
s =0.02s (1分)
=
=3
(1分)
即t2 —t1 = 3T +
T (1分)
∴ 波的传播方向沿
轴的负方向。 (1分)
注:没有写出
=8m,能T=
得出周期结果,可给2分
(2)∵ 波向右传播
∴t1 = 0s时位于x ="4" m处的质点的振动方向沿y轴正方向。 (1分)
又∵ (t2—t1 ) <![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817349202.gif)
∴ (t2 —t1) =
……① (1分)
波速
=
……② (1分)
①②有
=
=
= 26.7m/s (1分)
注:1、第(2)问,若波速与周期使用符号与第(1)问相同,可不扣分。
2、其他解法有道理的均给对应分数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817162197.gif)
(1)若v=400m/s
则:周期T=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817177332.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817208311.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817224287.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817240391.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817255223.gif)
即t2 —t1 = 3T +
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817255223.gif)
∴ 波的传播方向沿
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817146187.gif)
注:没有写出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817162197.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817177332.gif)
(2)∵ 波向右传播
∴t1 = 0s时位于x ="4" m处的质点的振动方向沿y轴正方向。 (1分)
又∵ (t2—t1 ) <
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817349202.gif)
∴ (t2 —t1) =
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817364374.gif)
波速
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817162193.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817396343.gif)
①②有
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817162193.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817427486.gif)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824121817442519.gif)
注:1、第(2)问,若波速与周期使用符号与第(1)问相同,可不扣分。
2、其他解法有道理的均给对应分数
![](http://thumb2018.1010pic.com/images/loading.gif)
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