8-mechanical wave(2009v1)
深入剖析SAW, BAW, FBAR滤波器
深入剖析SAW, BAW, FBAR滤波器很多通信系统发展到某种程度都会有小型化的趋势。
一方面小型化可以让系统更加轻便和有效，另一方面，日益发展的IC制造技术可以用更低的成本生产出大批量的小型产品。
MEMS(MicroElectromechanical System)是这种小型产品的相关技术之一。
MEMS 可以检测环境的变化并通过微型电路产生相关反应。
MEMS的主要部分包括sensor(微传感器)或actuator(微执行器)和transducer(转换装置)，其中sensor可以检测某种物理，化学或生物的存在或强度，比如温度，压力，声音或化学成分，transducer会把一种energy转换成另外一种(比如从电信号到机械波)。
目前MEMS被广泛的利用在多个领域里，如下图。
这篇文章主要说说MEMS的几种RF相关应用产品SAW,BAW, FBAR filter，也是目前手机中最常用的几种filter。
SAW,BAW和FBAR中，A都代表着Acoustic。
Acoustic wave中文翻译成声波，声波按频率分成3段，audio,infrasonic(次声波)和ultrasonic(超声波)。
Audio的频率为20Hz ~ 20KHz, 是人耳能听见的范围。
Infrasonic(次声波)是低频率，20Hz一下，人耳听不到，可以用来研究地理现象(比如地震)。
Ultrasonic(超声波)是20KHz到109KHz，也是人耳听不到的范围。
下面提到的声波都是超声波的范围，首先我们看看SAW filter。
Surface Acoustic Wave(SAW) filter顾名思义，SAW是一种沿着固体表面(surface)传播的声波(acoustic wave)。
一个基本的SAW filter由压电材料(piezoelectric substrate)和2个Interdigital Transducers(IDT)组成，如下图。
普通物理学机械波知识点总结(Summary of knowledge of mechanical waves in general physics)
普通物理学机械波知识点总结（Summary of knowledge ofmechanical waves in general physics）75. mechanical wave form: the vibration to a certain speed from the near to the distant in the elastic medium spread out.The 76. wave source and the elastic medium are two necessary conditions for generating mechanical waves.77. transverse wave: the direction of the particle vibration and the direction of wave propagation are perpendicular to each other.78. longitudinal wave: the direction of the vibration of the particles of the medium and the direction of wave propagation are parallel to each other.79. wave surface (in the same direction): in the wave propagation process, at any time, the medium vibration phase of the same point into the surface80. wave front (wave front): at some point the wave propagates to the front of the wave front.81. the wave whose surface is spherical is called spherical wave. The wave whose plane surface is plane is called plane wave. The wave whose surface is cylindrical is called cylindrical wave.82. make some arrow lines along the direction of the wave. This is called the wave line. The direction of the wave line indicates the direction of wave propagation. In an isotropichomogeneous medium, the wave line is perpendicular to the wave surface.83. simple harmonic: if the vibration propagates in the medium is the harmonic vibration, and the wave goes everywhere, in the medium each particle makes the same frequency, the same amplitude harmonic vibration, this kind of wave is called the simple harmonic. If the wave surface of a harmonic wave is plane, then such harmonic wave is called plane simple harmonic.84. the vibration equation of the particle: (A is amplitude, Omega is angular frequency, initial phase)85. wave function of plane harmonic wave (wave equation): (for any point at any point on the wave line, the particle of P is the displacement of harmonic vibration.86. wavelength (wavelength): the distance between two adjacent particles with a phase difference of 2 pi on the same wave line is called wavelength.The period of the 87. wave (T): the time required for the wave to travel one wavelength is called the cycle of the wave.The 88. wave frequency (V): reciprocal frequency period is called, in a unit of time, the number of full wave wave advance distance.89. a wave source with a certain period of vibration and frequency. The frequency and frequency of the waves induced in different media are the same, independent of the nature of themedium.90. the propagation velocity of vibration in medium is called wave velocity.91. (1) wave velocity is dependent only on the nature of the medium transmitted by the wave, irrespective of the frequency of the wave. (2) the frequency of wave is the same as that of vibration source, and it is independent of wave propagating medium. (3) the wavelength is related to the wave velocity and the frequency of the wave.92. important characteristics of the wave process: the propagation of mechanical energy with the propagation of waves.93. energy and velocity u propagate with the wave in a medium, in a homogeneous isotropic medium. The velocity and direction of propagation of energy are always the same as those of wave propagation and propagation. The above analysis can be used to say the wave propagation process, i.e., the propagation of energy.The energy density of the 94. wave: the energy of wave in a unit volume is called the energy density of the wave. (where p is the density of the medium, A amplitude, Omega is the angular frequency.)95. energy flux density: the average energy per unit area perpendicular to the wave velocity in a unit time is called the energy flow density of a wave. As the intensity of the wave flow density, short wave. The size and intensity of wave amplitudeis proportional to the square. Namely.Absorption of the 96. wave: when the wave propagates in the medium, the medium always absorbs some of the energy of the wave, so the intensity of the wave will gradually decrease. This phenomenon is the absorption of wave.97.: the Huygens principle moving in front of an arbitrary point can be regarded as secondary sources from the new wave, each point on the issue many times wave envelope formation, the new wave is the original surface in a certain period of time to spread.Diffraction of the 98. wave: when the wave encounters obstacles in propagation, its propagation direction changes. And can bypass the edge of the barrier and continue to move forward.The principle of superposition of wave 99.: in the meeting area, at any point of the particle vibration, vibration for the wave alone caused by vibration, that at any moment, the particle displacement is the wave when they are alone in the cause and displacement vector and.100. coherent waves: the superposition of waves with the same frequency, the same vibration direction, the same phase or the constant phase difference of two waves. The wave satisfying these three conditions is called coherent wave, and the source of coherent wave is called coherent wave source.101. standing wave: the amplitude and vibration direction and frequency of the two columns are the same, and the coherent waveof the opposite direction of the propagation is superposed to form a standing wave.102. Doppler effect: the phenomenon that the observer receives a different frequency from the source of the wave due to the movement of the observer (receiver) or the wave source two at the same time relative to the medium.The 103. wave sees movement: wave view static:104. the charge or charge system that does accelerated motion is the source of electromagnetic waves.105. accelerating electric charge or charge movement produces changes in the surrounding space, changes of the electric field are changing magnetic field, magnetic field and electric field change change, so to stimulate each other, with the passage of time, produced the propagation of electromagnetic waves in space, also called electromagnetic wave.One hundred and sixElectromagnetic wave is the vector wave of electric field intensity E and magnetic field intensity H.107. the basic characteristics of plane harmonic electromagnetic wave: (1) electromagnetic field vector E and H exist at the same location, have the same phase, and propagate at the same speed. (2) E and H are perpendicular to each other, and both of them are perpendicular to the direction of wave propagation. The three, E, H and u satisfy the right spiralrelation, which indicates that electromagnetic wave is transverse wave. The plane composed of E and H and their propagation directions is called the vibration surface of E and the vibration surface of H. E and H vibrate in their respective vibration surfaces respectively. This property is called polarization, and only S-wave has polarization. (3) at any point in space, there is a value between the E and the H:. (4) the propagation speed of electromagnetic wave depends on the dielectric constant and dielectric permeability of the medium.(5) electromagnetic waves reflect and refract at the interface of two different mediums. The ratio of the rate of electromagnetic wave in vacuum to C and the rate in a certain medium is called the absolute refractive index n of the medium, referred to as the refractive index..108. the energy that the electromagnetic wave carries is called radiation energy.109. unit time is transmitted by vertical electromagnetic wave. The radiation energy per unit area is called energy density, also known as wave intensity.110. the energy density of electric field and magnetic field are respectively:,. Therefore, the total energy density of the electromagnetic field is:111. in optics, the average energy density I is called light intensity:The 112. path is an equivalent amount of propagation time in the same or corresponding change under the same conditions, thelight propagation in the medium distance equivalent to corresponding distance of light in the air is spread, in value, equal to the corresponding refractive index optical path distance multiplied by the light propagation in the medium, in value, equal to the path the refractive index of the medium multiplied by the light propagation in the medium.113. luminous objects are called light sources.114. common luminescence processes: (1) thermal radiation (2) electroluminescence (3) photoluminescence (5) chemiluminescence.115. light: parallel interference of the same frequency and direction of vibration, harmonic wave beams of constant phase difference meet, overlap in some light, some synthetic intensity is higher than the intensity and divided, in other areas less than the intensity and synthesis of light intensity, light intensity of light intensity of interference fringes formed in synthesis phase, stable distribution in the space, called the interference of light. The superposition of light waves is called coherent superposition, and coherent beams can be generated by coherent superposition of two beams of light. The condition of coherent superposition is called coherent condition. If the two beams of light do not satisfy the coherent superposition condition, in the overlapped region of the light wave, the synthetic light intensity is equal to the sum of the intensity of the points, and no interference occurs, at which point the superposition of two beams of light is called incoherent superposition.116. the interference conditions of two beams are as follows: (1) the same frequency; (2) the phase difference is constant;(3) the vibration direction of the optical vector is parallel.117., the optical path is a converted quantity. When the time of propagation is the same or the phase changes the same, the distance of light propagation in the medium is reduced to the corresponding distance of light propagation in vacuum. Numerically, the optical path is equal to the refractive index of the medium multiplied by the path of light propagating in the medium.118. equal thickness interference fringes: the same interference fringes in the interference pattern correspond to the same thickness on the film.119. Newtons ring: fringes formed by interference of light reflected from the upper and lower surfaces of the ring air wedge. It is waiting for interference fringes.The diffraction of 120. beams is usually divided into two categories: Fresnel diffraction (near field diffraction) and Fraunhofer diffraction (far field diffraction).121. Huygens Fresnel principle: the secondary waves from each point of the same wave surface are coherent waves, and the superposition of them at a certain point in space is coherent superposition.122. using the principle of multi slit diffraction, the component of chromatic dispersion is called diffractiongrating.123. the light vector is limited to a single direction and the light is called polarized light.124. Marius's Law: if the intensity of polarized light is light, the light intensity of projection light is I. The angle between the optical vector, the vibration direction of the a polarized light and the polarization direction of the analyzer.125. when a beam of natural light is incident into an anisotropic medium, the refracted light at the interface is broken into two different refracted beams in the direction of propagation.126. the two beams of refraction have the following characteristics: (1) two beams of refracted light are linearly polarized light in different directions in the direction of the light vector. (2) one of the refracted beams is always in the incident plane and follows the refraction theorem, which is called ordinary light. The other beam is not in the incident plane, and does not obey the law of refraction. It is called extraordinary light.Two basic assumptions: 127. chivalrous relativistic (1) in all inertial reference frame, all physics theorem has the same form, which has the same mathematical expressions, or, for the description of all physical phenomena rule, all inertial systems are equivalent. This is also called the relativity principle of chivalry relativity. (2) in all inertial frames,In the light of vacuum rate along each direction transmission are equal to the same constant C, independent motion with the light source and the observer, which is also known as the principle of constant speed of light.128., it is supposed that the energy of the particle is static and is called stationary energy (static energy). It is the total energy of particle remote control, and the difference between the two is the energy added by the particle because of its movement, that is, energy129. thermal radiation: electromagnetic radiation of an object as determined by its temperature.130. equilibrium heat radiation: when the radiation and absorption are in equilibrium, the temperature of the object is no longer changing and is in a state of thermal equilibrium.The greater the radiation power of 131. objects, the greater their absorption capacity, and vice versa.132. absolute blackbody (short for blackbody): an object that absorbs all kinds of radiation at all wavelengths without reflecting or projecting completely.133. photon Einstein hypothesis: a beam of light beam at the speed of light is a telecontrol of the particles, these particles called photons; each photon frequency of light with energy, he can not only the segmentation, is absorbed or produced.134. photoelectric effect equation:135. the relationship between the voltage and the maximum initial energy of photoelectronsRed limit of 136. photonThe relation between the momentum electron volt of 137. photon and Joule 1v=1138. Planck constant139. the fluctuation of light: light has fluctuation and has particle property.140. photoelectric effect: the emission of electrons by metals and their compounds under light irradiation.141. De Broglie hypothesis: not only has light wave particle duality, all physical particles such as electrons, atoms and molecules also have wave particle duality.142. laser is based on stimulated radiation amplification principle of a coherent light radiation.。
慢走丝线切割放电状态在线识别新方法
慢走丝线切割放电状态在线识别新方法陈良【摘要】在慢走丝电火花线切割加工过程中,由于其放电机理的复杂性、放电点的随机性和最优加工参数的不确定性,放电加工过程中的放电间隙电压可大致分为开路、正常放电、电孤、短路和复杂放电五种放电波形.在不同加工参数下,各类放电波形的比例不一样,不适当的加工参数将显著降低正常放电波形的比例,严重影响慢走丝加工过程中的效率、精度和稳定性.建立一种慢走丝线切割放电状态浮动电压阈值在线识别方法,在放电波形识别系统中,根据不同的加工工况,调节阈值电压的参考值.再根据识别的各种放电波形的比例,采取相应的措施,改变加工参数,已达到最优的放电波形比例.实验数据表明,该系统具有较高的识别精度、实时性和稳定性,且提高材料去除率约20％,降低表明粗糙度约27％,该放电波形识别系统可在电火花线切割加工中具有较好的实用性.【期刊名称】《机械设计与制造》【年(卷),期】2017(000)002【总页数】4页(P128-131)【关键词】慢走丝线切割;放电波形;在线识别;浮动阈值【作者】陈良【作者单位】中州大学机电与汽车工程学院,河南郑州450044【正文语种】中文【中图分类】TH16;TP39随着新型材料引进到现代制造业，如高强度、高硬度和高耐磨性等，电火花线切割加工方式应运而生，由于其具有能够加工各种硬度和复杂形状工件的能力，且具有较高的效率和精度，广泛应用于模具、电子、汽车和航空航天等制造领域。
按照电极丝的走丝速度，线切割可以分为高速往复走丝线切割（6~12）m/s、中速往复走丝线切割（1~2）m/s和慢速单向走丝线切割（0.1~0.2）m/s。
上世纪70年代，高速往复走丝线切割首次被第三机械工业部研发成功，快速占领了国内电加工制造领域；随着零件要求的提高，中速往复走丝线切割逐步取代了高速往复走丝线切割的市场地位。
慢速单向走丝线切割具有更高的加工精度和表面质量，但中国大陆的技术还不够成熟，主要依靠进口日本、瑞士和台湾的产品。
平面简谐波
解：
200 = 50Hz 0.02 ν= = λ 4 u
y (m) u = 200m·s-1 t = 0 时波形 x (m) o
1 2 3 4 5
ω = 2πν = 100πs −1
为方便起见 , 以下均 用 SI 制 , 单位略去。
λ = 4m
ω = 2πν = 100πs
解： O 点振动方程 (1) y = A cos (ω t + ϕ 0 )
地震波分为纵波和横波。纵波每秒钟传播速度5~6 千米，能引起地面上下跳动；横波传播速度较 慢，每秒3~4千米，能引起地面水平晃动。由于纵 波衰减快，离震中较远的地方，只感到水平晃动。 在一般情况下，地震时地面总是先上下跳动，后 水平晃动，两者之间有一个时间间隔，可根据间 隔的长短判断震中的远近。
11-2 平面简谐波的表达式 (波函数)
例 横波沿一张紧的长绳传播，波动表达式为： y=0.04cosπ(5x200t)。求（1）A , ν , λ , u ;（2）如每米弦的质量为0.05kg·m-1， 求绳中张力。（例11-1） 解：将表达式写成标准形式
t x y = 0.04 cos 2 π( − ) 1 / 100 2 / 5 A = 0.04m T = 0.01s
t x y＝A cos[2π ( + ) + ϕ 0 ] T λ 2π y＝A cos[ (ut + x) + ϕ 0 ]
λ y = A cos(ω t + kx + ϕ 0 )
二、波函数的物理意义 二、波函数的物理意义
1、x一定，则位移仅是时间 的函数，对于x=x0 2πx0 ⎞ ⎛ + ϕ0 ⎟ y = A cos⎜ ωt − λ ⎠ ⎝ 表示x0处质点的振动方程
大学物理_波动学基础
a T a Y
T：绳的张力
杆的纵向微振动波
杆的横向微振动波 声音在空气中传播 真空中的电磁波
Y：杨氏弹性模量
a G
G：切变弹性摸量 B：体变模量
a
B
a
0 0 ０真空介电常数，０真空磁导率
1
《大学物理》课件
介质的几种典型模量
(1).杨氏模量 若在截面为S，长为l的细棒两端加上大小相等、方向相反 的轴向拉力F，使棒伸长l，实验证明：在弹性限度内，正应 力F/S与线性应变l/l成正比，即
y Acos( t
l
u
)
《大学物理》课件
例题2-4 波沿x轴正向传播，A=10cm, =7rad/s; 当t=1s时, ya=0, a<0, yb=5cm,b>0 。设>10cm, 求该波 的波动方程。 y x ) o ] (t 解 y Acos[ u u
o
3.波长 — 一个周期内波动传播的距离。
u
T
4.平面简谐波—波面为平面，媒质中各质点 都作同频率的简谐振动形成的波动。本章主要讨 论这种波。
《大学物理》课件
1 1 例题2-1 已知： y 0.5cos ( t x )(SI), 2 2 求：(1)波的传播方向，A、T、、u，原点 的初相； (2) x=2m处质点的振动方程，及t=1s时质点 的速度和加速度。 (3)x1=1m和x2=2m两点的相差。
· ·· · · · · t · · · ·· · ·
u t 平面波
球面波
惠更斯原理的不足：不能求出波的强度分布； 不能解释后退波问题等。
《大学物理》课件
§5.2 平面简谐行波的波动方程 !
探讨机械波振动方向的判断方法
探讨机械波振动方向的判断方法机械波既是高中物理学习的重点，也是难点，特别是如何确定波动质点的振动方向。
为了有效突破这一难点，使学生掌握机械波的运动特征，弄清波动与振动的联系与区别，我们引导学生进行了大量探究活动，总结出以下四种确定波动质点振动方向的方法，供参考。
Key, mechanical wave is the high school physics learning is difficult, especially how to determine the direction of vibration wave particle. In order to overcome this difficulty, to enable students to master the movement characteristics of mechanical wave, and to clarify the difference of wave and vibration, we guide students to a large number of research activities, summed up the following four determine the wave vibration direction method, for reference.方法一波的成因法Method causes a wave method由波的形成原理可知，后振动的质点总是重复先振动的质点的运动，而当质点处于波峰和波谷瞬间，其速度为零。
若已知波的传播方向，判断某质点的振动方向时，可找沿波传播方向与该点距离最近的波峰或波谷，根据波峰或波谷位置的关系确定振动方向。
The formation principle of the wave, the particle vibration always repeat the first vibration of the particle motion, and when the particle at the crest and trough moment, its velocity is zero. If the propagation direction of waves to determine the direction of vibration is known, a particle, can be found along the propagation direction and the distance to the nearest peak or trough, determine the direction of vibration according to the position of the peak or trough.例1 如图1所示，波沿x轴正向传播，试确定该时刻b、d两质点的振动方向。
窄带滤光片指标
窄带滤光片是一种光学元件，它允许特定波长范围内的光通过，而阻止其他波长的光。
这种滤光片通常用于光谱分析、激光应用、光纤通信、医疗诊断和其他需要精确控制光波长的场合。
窄带滤光片的指标包括以下几个方面：1. 中心波长（Central Wavelength, CWL）：- 这是滤光片透过率最高的波长。
窄带滤光片的中心波长通常非常精确，可以在很小的范围内调整。
2. 透过带宽度（Bandwidth）：- 这是指滤光片允许通过的光波长范围，通常以全宽半高（Full Width Half Maximum, FWHM）来表示。
窄带滤光片的带宽很窄，通常在几纳米到几十纳米之间。
3. 透过率（Transmittance）：- 这是滤光片对特定波长光的传输效率。
理想的窄带滤光片在中心波长附近的透过率非常高，通常可以达到90%以上。
4. 截止深度（Blocking）：- 这是滤光片阻止非透过带光的能力。
窄带滤光片的截止深度通常很高，可以达到OD6（光学密度6）或更高，这意味着它能够非常有效地阻止非目标波长的光。
5. 波前质量（Wavefront Quality）：- 这是指滤光片输出光的波前形状。
高质量的窄带滤光片应该产生尽量平滑的波前，以减少光学系统的像差。
6. 偏振依赖性（Polarization Dependence）：- 某些滤光片可能会对光的偏振状态有特定的要求，这可能会影响其性能。
7. 环境稳定性（Environmental Stability）：- 滤光片在不同温度、湿度和压力条件下的性能稳定性。
对于窄带滤光片，环境稳定性通常非常重要，因为它们用于精确的光学应用。
8. 机械稳定性（Mechanical Stability）：- 滤光片在物理安装和操作中的稳定性，包括其对温度变化的抵抗能力。
9. 抗反射涂层（Anti-Reflection Coatings）：- 为了减少滤光片表面的反射损失，通常会在其表面涂覆抗反射涂层。
1波函数的建立重点
z
波面
x
球面波 柱面波
y
波线
在各向同性均匀媒质中，波线⊥波面。
平面波 波 线 波 面
波 线
球面波
波 面
波阵面为一平面
波阵面为一球面
四 、波的分类 机械波（ mechanical wave ） 按波的性质 按波线与振动 方向关系 电磁波（electromagnetic wave ） 横波（transverse wave ） 纵波（longitudinal wave ）
任一波例如，水波、地表波，都能分解为横波与纵波来进 行研究。
横波：质点振动方向与波的传播方向相垂直的波. （仅在固体中传播 ）
特征：具有交替出现的波峰和波谷.
纵波：质点振动方向与波的传播方向互相平行的波.
（可在固体、液体和气体中传播）
特征上游”的质点依次带动“下游”的质点振动。 (2) 质点并未“随波逐流”，波的传播不是媒质质点 的传播，各质点仅在自己的平衡位置附近振动。 (3) 某时刻某质点的振动状态将在较晚时刻于“下游 ”某处出现，波动是振动状态——振动相位的传播。 沿波的传播方向， 各质点的相位依次落后。 说明：
8.1 机械波的产生和传播
一、 机械波的产生 机械波: 机械振动以一定速度在弹性介质中由近及远地 传播出去，就形成机械波。 条件
｛
波源：作机械振动的物体
弹性介质：承担传播振动的物质
二、 横波和纵波
横波：介质质点的振动方向与波传播方向相互垂直的波； 如柔绳上传播的波。
介质质点的振动方向和波传播方向相互平行的波； 纵波： 如空气中传播的声波。
求 (1) 波的振幅、波长、周期及波速；
(2) 质点振动的最大速度。
解 (1) a. 比较法(与标准形式比较） 标准形式 波函数为 比较可得
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y o
a
x
t t0
x
Deduce the wave equation
(1). the wave travels in the positive direction of axis X
y o
a x
x
The axis X is a wave line.
If the harmonic vibration function of medium element at the origin is
wave velocity: the propagation velocity of wave
u
T
The wave velocity depends on the characters of medium.
T u
u
medium Wave source
4. Planar Simple Harmonic Wave
t0
t T / 4
t T / 2
t 3T / 4
t T
t 5T / 4
conclusion
Later medium element in the harmonic wave always repeats the vibration state of the wave source . The medium element does not go with the wave. The medium element vibrates only about the equilibrium position. The wave is the propagation of vibration state and vibration energy without the transfer of mass . The phase of each medium element along the propagation direction of wave successively decreases at the same instant. This conclusion is called the principle of successive phase decrease. It is the theoretical basis to construct harmonic wave function for us.
y0 A cos(t 0 )
(a) time delay
y
O
u
x t u
x
x
p
x y A cos[ (t )＋0 ] u
(b) phase delay
It is often useful to express the phase difference between the two points in terms of a fraction of the wavelength. Because a difference of one wavelength corresponds to a phase difference of 2π rad, an arbitrary shift Δr in position of one point with respect to another is related to the phase difference as follows:
Wave Shape Illustration
Embody the displacement away from equilibrium position of the vibrators at different equilibrium position in the same disonic Wave Function Energy of Harmonic Wave
Huygens Principle
Superposition and Interference of Waves Standing Wave
Preface
Wave is an important form of motion. The classifications of wave: 1. Mechanical Wave: the propagation of mechanical vibration in continuous medium. Sound wave, Seismic wave, water wave…… 2. Electromagnetic Wave: the propagation of electric field and magnetic field in space. Play： Electromagnetic waves are a special class of waves that do not require a medium in order to propagate. 3. Matter Wave : wave is one of the most important attributes of the microscopic particles . Play：
The reciprocal of period is called the frequency of wave, which usually written as v .
1 T
Obviously, the frequency of wave equals the vibration frequency of medium element, they equal the frequency of the wave source.
The formation of mechanic wave Wave source Continuous medium Two conceptions: A transversal wave: the wave whose vibration axis is perpendicular to the wave line . A longitudinal wave: the wave whose vibration axis paralleled to the wave line . Play flash
2
x
(b) phase delay the vibration equation at origin O:
y
O
u
y0 A cos(t 0 )
x
x
p
The wave equation of x position:
2x yp A cos t＋0 （ )
(2). the wave travels in the negative direction of axis X.
General Characters of Wave : speed energy The propagation of vibration state reflection, interference, diffraction Similar wave function ……….
1. The Formation and Propagation of Mechanical Wave
spherical wave
cylindrical wave
plane wave
3. Representation in time-space: Wavelength, Period and Wave Velocity
Wavelength
If the phase difference between two points on the wave line equals 2 , the distance between the two points is called the wavelength, which usually written as .
When the medium is uniform, the vibration rule of medium element is the same as the wave source. The amplitudes of every element are equal without damping. If the wave source does simple harmonic vibration , the medium element does simple harmonic vibration also.
2. Representation in geometry
Wave Field Wave Surface Wave front The phase of wave front equals the phase of wave source. Wave line The straight line denoted the propagation direction of wave is called the wave line .
(1) Definition : Wavefront: planar Wave source does simple harmonic vibration. Since any wave may be considered as the superposition of various harmonic waves, the concept of harmonic wave is the theory basis to study various real waves. (2) Suppose :
A transverse wave is a wave in which the particles of the medium move in a direction perpendicular to the direction of the wave velocity. An example is a wave along a stretched string. Longitudinal waves are waves in which the elements of the medium move back and forth parallel to the direction of the wave speed. Sound waves in air are longitudinal.