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第十四章  机械波
文章来源:本站原创   点击数:7662   更新时间:2008/2/25 15:02:21

1.横波  V14-1(和正文)

横波是质点振动方向与波的传播方向相垂直的波,其外形特征是交替出现凸起的波峰和凹下的波谷。

V14-1

The transverse wave is the wave in which the particles, vibration is perpendicular to the wave′s direction of travel.

Its external shape property is that the projecting crest and the hollow trough appear alternately.

1VM14-3复合波任何非简谐的复杂的波都可看成是由若干个频率不同的简谐波叠加而成的。该动画是由频率和振幅各不相同的三个简谐波叠加成复杂波的情形。

VM14-3

Any complex wave can be resolved into a series of simple harmonic waves with different frequencies.

On the animated drawing a complex wave is resoleved into three simple harmonic waves with different frequencies and amplitudes. 14-1

2.纵波(正文)

质点的振动方向与波的传播方向相互平行的波,称为纵波,如一根水平放置的长弹簧,如果某一部分因受到水平外力的作用而振动,各部分弹簧就依次左右振动起来,并沿着弹簧长度的方向传播,它的外形特征是弹簧出现交替的“稀疏”和“稠密”区域。

The wave in which the motion of the particles is parallel to the direction of the wave′s travel is called longitudinal wave. Its external shape property is that the sparse and the dense areas appear alternately.14-2

3.机械波的传播(正文加P2

无论是横波还是纵波,它们都只是振动状态(即振动相位)的传播,弹性介质中各质点仅在它们各自的平衡位置附近振动,并没有随振动的传播而流走。

No matter whether it is transverse wave or longitudinal wave.They are just the propagation of the state of the vibration (That is,the phase of the vibration).Each particle in the elastic medium is only vibrating near their equilibrium position.They don’t flow with the propagation of the vibration.14-3

4.波函数的意义(正文)(配音不全)

波函数的物理意义:

1)当 一定时(即波线上的某一点),则 仅为时间 的函数,此时,波函数表示的是距原点 处的质点在不同时刻的位移,即该质点做简谐运动的情况。

2)当 一定时,(即某一瞬时), 轴上所有质点的位移 仅为 的函数,此时,波函数表示了给定时刻各质点的位移分布情况。(以 为纵坐标, 为横坐标,可得如上图所示的不同时刻的 曲线,该曲线也叫波形图。从波形图可以看出,经过一个周期的时间,波向前传播了一个波长的距离)

3)当 都变化时,波函数就表达了所有质点位移随时间变化的整体情况。

When x is a centain value (That is ,a certain point on the wave line),y is only the function of time .So the wave function expresses that it is the displacement of particle which is from point .That is,the particle is in a SHM.14-4

5.惠更斯原理(正文P9

介质中波动传播到的各点都可以看作发射子波的波源,而在其后的任意时刻,这些子波的包络就是新的波前,这就是惠更斯原理。

In 1679 Duch physicist Huygens (C.Huygens,1629-1695)first advanced:In the medium all points on a wave front serve as point sources of spherical secondary wavelets.

After an arbitrary time, the new position of the wave front will be that of a surface tangent to these secondary wave lets.

This is Huygens principle.14-5

6.用惠更斯原理求波前   VM14-8

图中所表示的是以O为中心的球面波以波速 在介质中传播,在时刻 的波前是半径为 的球面 ,根据惠更斯原理, 上的各点都可以看成是子波波源,以 为半径画出许多半球形子波,那么,这些子波的包络 即为 时刻的新的波前。显然, 是以O为中心,以 为半径的球面。如法炮制即可不断获得新的波前。

半径很大的球面波上的一部分波前,可以看作是平面波的波前,用惠更斯原理同样可求得其波前。

VM14-8

Find the wave front by applying Huygens principle, on the animated drawing a spherical wave travels with the center at point O in the medium.

Its wave speed is u. At time t its wave front is a sphere.  whose radius is R. According to Hugyens principle, each point on  can be regarded as sources of the secondary wavelet. Draw many semispherical wavelets with radius .

The surface  tangnent to these Secondary wavelets is the new wave front at time that. Obviously,  is a sphere.Its center is at point o and its radius is .Follow suit,we can continuously obtain the new wave front

A portion of the wave front of a spherical wave whose radius is very large can be reigned as the wave front of a plane wave.

We can alike find the wave front by applying Hugyens principle.14-6

7.波的衍射 VM14-9

平面波到达一宽度与波长相近的缝时,缝上各点都可看作是子波的波源。作这些子波的包络,就得出新的波前。很明显,此时波前与原来的平面略有不同,靠近边缘处,波前弯曲,即波绕过了障碍物而继续传播。

VM14-9 diffraction of waves.

When a plan wave encounters a slit,whose width is close to the wave length,each point on the slit serves as the source of the wavelets.

Draw a surface tangnent to these wavelets, you can get the new wave front.Obviously,there is a little difference between the new wave front and the former plane.The part of the wave front near the edge is winding.

That is ,the wave continues propagating through the barrier.14-7

8.波的衍射现象(正文P10

衍射现象显著与否,是和障碍物(缝、遮板等)的大小与波长之比有关的,若障碍物的宽度远大于波长,衍射现象不明显;若障碍物的宽度与波长差不多,衍射现象就比较明显;若障碍物的宽度小于波长,则衍射现象更加明显。

P10 It is related with the radio of the size of the barrier (slit,board arrier etal)to the wave length whether the diffraction phenomenon is marked.If the width of the barrier is larger than the wavelength,the diffraction phenomenon isn’t marked.If the width of the barrier is close to the wavelength,the diffraction phenomenon is fairly marked ,If the width of the barrier is smaller than the wavelength,the diffraction phenomenon is more marked.14-8

9.波的叠加原理(正文)(P10

研究几列波同时在介质中传播并相遇时,介质中质点的运动有如下的规律:

1)几列波相遇之后,仍然保持它们各自原有的特征(频率、波长、振幅、振动方向等)不变,并按照原来的方向继续前进,好像没有遇到过其他波一样。

2)在相遇区域内任一点的振动,为各列波单独存在时的该点所引起的振动位移的矢量和。

上述规律叫做波的叠加原理。

P10 1.After (a series of )wave meet,they still keep their respective initial properties(frequency,wavelength,amplitude,the direction of the vibration and so on)and continue on their way undisturbed,as if the other were not present.

2.In the area in which they meet,the displacement of any point is the sum of the displacement of any point is the sum of the displacements that the point would experience if each wave traveled alone.

This is principle of superposition for waves.14-9

10.两列波的相遇  V M14-10

两列振动方向平行的波,在同一直线上相向传播,在两波相遇处各点的位移,是两列波各自引起的振动位移之和;而在相遇之后,则仍以各自原来的波形继续传播,就像它们没有相遇过一样。

VM14-10

Two waves,whose sources oscillate in the same direction,propagate in opposite direction along a line.The displacement of each point when the waves overlap is the sum of the displacements that the point would experience if each wave travels alone.After meeting ,each wave continues on their way,undisturbed,as if the other were not present.14-10

11.波的干涉现象(正文P10

人们把频率相同、振动方向平行、相位相同或相位差恒定的两列波相遇时,使某些地方振动始终加强,而使另一些地方振动始终减弱的现象,叫做波的干涉现象,能够产生干涉现象的两列波叫做相干波,而它们的波源就叫做相干波源。

P10 Suppose two waves which have the same frepuency,oscillate in the same direction and have the same phase or a constant phase difference meet with each other.You can see that some points have maximum amplitude.Some other points have minimum amplitude.This phenomenon is called interference of waves.The two waves which can create interference are called interference are called coherent waves.Their sources are called coherent sources of waves.(14-11)

12.驻波(正文P14

驻波是由振幅、频率和传播速度都相同的两列相干波,在同一直线上沿相反方向传播时叠加而成的一种特殊形式的干涉现象。

P14 Two coherent waves which have the same amplitude,frequency and wave speed propagate in opposite direction along a line.So they overlap is a special interference phenomenon.(14-12)

13.驻波的特征(正文P15

波节两边各点同时沿相反方向达到各自位移的最大值,又同时沿相反的方向通过平衡位置;而两波节之间各点则沿相同方向达到各自的最大值,又同时沿相同方向通过平衡位置,可见弦线不仅作分段振动,而且各段作为一个整体,一齐同步振动,在每一时刻,驻波都有一定的波形,但此波形既不左移,也不右移,各点以确定振幅在各自的平衡位置附近振动。这些性质与前面所讲的行波不同,因此叫做驻波。

P15 The corresponding particles in two adjacent sections teach their maximum displacement at the same time but in opposite directions.Silmilarly,they also pass through their equilibrium position at the same time but in opposite directions.But the particles between the adjacent nodes reach their maximum displacement at the same time in the same direction.They also pass through their equilibrium position at the same time in the same direction.(14-13)

14.相位突变(半波损失)(正文P15

波在固定点B处反射,并形成了波节:这说明入射波与反射波在此处的相位时时相反,即反射波在分界处的相位较之入射波跃变了 ,相当于出现了半个波长的波程差,通常把这种现象称为相位跃变 ,有时也形象地叫做“半波损失”。

P15 In the experiment as shown in Fig.14-7,the incident wave is reflected at B,which is a fixed point,forming a node.This indicates that the phase of oscillation caused by the incident wave is in opposition to that caused by the reflected wave,that is to say,the wave undergoes a phase change of  when it is reflected at a fixed end.This fact is usually called“phase shift”.It is also called“half-wave loss”(14-14)

15.多普勒效应(正文)(P18

当波源与观察者同时相对介质运动时,观察者所接受到的频率为

上式中观察者向着波源运动时, 前取正号,远离时取负号,波源向着观察者运动时, 前取负号,远离时取正号。

P18 When the observer and the source are simultaneously moving to the medium,the received frequency is

If the observer moves towards the source,the sign on  is plus in the above-mentioned equation.If he moves away,the sign is minus.

If the source moves towards the observer.The sign on  is minus.If it moves away,the sign is plus.(14-15)

16.电磁波(正文)

电磁波主要特征

1)电磁波是横波

2 同相位,在任何时刻,任何地点电磁波的 都是同步变化的

3 的大小成正比

P20 1.Electromagnetic waves are transverse waves.

2. and  have the same phase.

The changes of and  of the electromagnetic is synchronous at any time and at any locality.

3.The magnitude of  is  proportional to that of .(14-16)

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