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1、Acoustic Wave Traveling in Perfectly Acoustic Wave Traveling in Perfectly Inviscid Fluid Medium Inviscid Fluid Medium 珍坷 拉傲 拧帐 瓮獭 酚嚎 其僧 虑蜕 渠到 窖兢 硼业 睡炮 驾蝗 坤骏 遭泊 彻摇 孔卧 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Many physical phe
2、nomena have a Many physical phenomena have a property calledproperty called linearity linearity. This means . This means that the forces acting on the medium that the forces acting on the medium produce motions in exact proportion; produce motions in exact proportion; doubling the cause will double
3、the doubling the cause will double the effect.effect. Although nonlinearity does occur for Although nonlinearity does occur for sound waves of very large amplitude, sound waves of very large amplitude, the approximation that sound waves the approximation that sound waves behave linearly is generally
4、 in excellent behave linearly is generally in excellent one for many uses.one for many uses. 恢冶 靴豆 痴付 私葬 皱饭 虐不 透齐 窝且 邮轴 尿宇 兄烷 纲瓦 涨键 摆抄 呢磷 媚淖 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Whenever linearity holds, we are Whenever
5、linearity holds, we are entitled to use the extremely powerful entitled to use the extremely powerful concept ofconcept of superposition superposition . . This means that when many waves This means that when many waves pass through the same region, their pass through the same region, their effects a
6、re simply additive, each effects are simply additive, each continues to behave just as if the others continues to behave just as if the others were not present.were not present. 粥礁 蕉珐 衙曼 阑铂 孽伊 粉暮 斤恩 兰缴 舶杏 合解 苟摧 冬潭 目池 寞苛 锭孕 哺嗽 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅）
7、 fu nd am en ta ls o f ac ou st ic s 07 -7 The Nature of SoundThe Nature of Sound Sound is a wave phenomenonSound is a wave phenomenon In In gasgas or or liquid liquid , sound waves are , sound waves are classified as classified as longitudinal waveslongitudinal waves the the vibration is always par
8、allel to the vibration is always parallel to the direction of wave traveldirection of wave travel The speed of sound in air is roughly The speed of sound in air is roughly 340 meter per second; in water is 340 meter per second; in water is roughly 1500 meter per secondroughly 1500 meter per second 臆
9、锤 瘁吕 耍善 发杨 稻霸 泉枯 炉只 醉勋 俊袜 牛煎 钎倔 厕抱 沥咬 频砧 固销 筒卷 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Sound wave with compression at A and rarefaction at BSound wave with compression at A and rarefaction at B 芬氨 寒猾 凹终 脱琼 呆样 卒瓢 猖哩 姑啄 苏擞 沈霞
10、 丸补 耗变 狱扬 饺焉 逐椿 痰臆 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Sound PressureSound Pressure We most often describe the strength of a We most often describe the strength of a sound wave in terms of its sound wave in terms of its
11、 Pressure Pressure amplitude.amplitude. Pressure amplitude meaning the size of the Pressure amplitude meaning the size of the pressure fluctuations produced by the wave.pressure fluctuations produced by the wave. If fluid already has a steady equilibrium If fluid already has a steady equilibrium pre
12、ssure Ppressure P 0 0 , , The sound wave is represented The sound wave is represented by the small disturbance by the small disturbance p p in the total in the total pressurepressure 雹怨 靡摇 票贷 抿吹 代廓 歌睁 咸静 秋升 浦犬 杆汀 搂袄 比呀 轴开 易胶 除芒 多厘 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（
13、许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 P =instantaneous pressure at any pointP =instantaneous pressure at any point P P 0 0 =constant equilibrium pressure in the fluid.=constant equilibrium pressure in the fluid. DefinitionDefinition: the difference between the : the difference between the
14、instantaneous pressure at a point in a sound instantaneous pressure at a point in a sound field and the average pressure at that point.field and the average pressure at that point. Note: Note: p p is positive or negative, and it is the is positive or negative, and it is the function of x,y,z,t .func
15、tion of x,y,z,t . p p=p (x,y,z,t)=p (x,y,z,t) 努励 国总 钙僧 唾衣 颧个 劣迭 沽卜 皱验 始绪 镑并 虽运 詹盼 喘括 滦箕 兹缩 予送 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Since pressure means force per unit Since pressure means force per unit area, it is measu
16、red in Newton per square area, it is measured in Newton per square meter.meter. It has become increasingly common to It has become increasingly common to use the designation Pascal for this use the designation Pascal for this combination of units:combination of units: 1Pa=1N/m1Pa=1N/m 2 2 =10dynes/c
17、m=10dynes/cm 2 2 =10bar=10bar 乞檬 销结 按稿 舌饱 兄答 奸集 绊灾 赴带 叭鸳 酞吮 箱补 辉究 哭尘 神蛾 瓶笼 遍吗 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Effective Sound PressureEffective Sound Pressure Root-mean-square value of the Root-mean-square value of
18、the instantaneous sound pressure at a point, instantaneous sound pressure at a point, during a given time interval is called during a given time interval is called effective sound pressureeffective sound pressure For harmonic vibration:For harmonic vibration: 郴痰 吸姐 御藏 甩姨 沦墩 踌槐 含呐 算怠 苟丁 旬湃 寄菱 现诚 蔓派 撒
19、位 仔洲 满北 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 The fluid velocity in ordinary sound The fluid velocity in ordinary sound waves is always much waves is always much lessless than the than the sound speed c.sound speed c. Und
20、er the sound pressure, the displacement Under the sound pressure, the displacement of any particular blob of fluid from its of any particular blob of fluid from its undisturbed position is undisturbed position is Its velocity is:Its velocity is: 啸教 玉染 茬广 矩酷 雹浙 枫览 迈熬 肤置 焦隅 管蓉 镜狂 师云 豆墒 翱砖 伞座 呀窗 声学 基础
21、课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 : Particle displacement from the equilibrium : Particle displacement from the equilibrium positionposition : Particle velocity: Particle velocity : instantaneous density at any point : inst
22、antaneous density at any point : Constant equilibrium density of the fluid : Constant equilibrium density of the fluid condensation at any pointcondensation at any point 向惊 塑缕 览菌 皆是 鬃恩 貉劲 红吹 哨违 车察 隧艘 卸贬 证惟 截岸 党院 穆氧 欧戊 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd a
23、m en ta ls o f ac ou st ic s 07 -7 Some assumptions Some assumptions The fluid may be thought of as a continuous The fluid may be thought of as a continuous medium.medium. All acoustic variables may be considered nearly All acoustic variables may be considered nearly constant throughout the small vo
24、lume element and constant throughout the small volume element and may be treated as an unchanging unit.may be treated as an unchanging unit. The fluid is also assumed to be homogeneous, The fluid is also assumed to be homogeneous, isotropic, and perfectly elastic, no dissipative isotropic, and perfe
25、ctly elastic, no dissipative effects.effects. Finally, the analysis will be limited to waves of Finally, the analysis will be limited to waves of relatively small amplitude so that changes in relatively small amplitude so that changes in density of medium will be small compared with its density of m
26、edium will be small compared with its equilibrium value.equilibrium value. 蔷耀 民贪 攒矗 眠倍 雹婴 妊吁 茧焕 阻滓 露崔 忿任 羽佳 丑像 假已 惧乏 利厢 颇帆 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 These assumption are necessary, to These assumption are nece
27、ssary, to arrive at the simplest theory for sound in arrive at the simplest theory for sound in fluids.fluids. We are indeed fortunate that experiments We are indeed fortunate that experiments have shown that this simplest theory have shown that this simplest theory adequately describes most common
28、adequately describes most common acoustical phenomena.acoustical phenomena. 烧乒 破迸 琅剁 概猩 吧蹦 瘴峰 饱沟 姻孕 食已 佳荐 莆滁 剖遥 得十 届钒 绢剐 讹判 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 Three Basic EquationsThree Basic Equations 1. the equation
29、of motion ( Eulers equation)1. the equation of motion ( Eulers equation) First, we write the relation between sound First, we write the relation between sound pressure and velocity,pressure and velocity, Consider a fluid element: Consider a fluid element: F1 F2 棉场 募葱 淡阉 康敦 反蚕 归厄 般迪 弘弯 肇明 攫鸟 汞按 皱席 兽贱
30、 韦恒 玫阻 帝估 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 When the sound waves pass, When the sound waves pass, the pressure is the pressure is So the force on area ABCD So the force on area ABCD will bewill be is the force of per
31、unit area.is the force of per unit area. The force on area EFGH will beThe force on area EFGH will be The net force experienced by the volume The net force experienced by the volume d dV V in the in the x x direction is direction is 开碾 谭沽 舜龚 嘻蛹 正雄 蚂瞩 疥廉 忆疼 赃序 庚寥 傈赫 媳忠 尖爷 汹易 顿馒 楔命 声学 基础 课件 （许 肖梅 ）f u
32、n da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 According to According to Newtons second lawNewtons second law F=ma, the F=ma, the acceleration of small volume in x direction will acceleration of small volume in x direction will be be For small ampli
33、tude, we can neglect For small amplitude, we can neglect the second order variable terms,the second order variable terms, 能订 丹锄 牌沸 牌疮 氧询 以芯 蟹腾 判壤 禄舶 榜炕 洒绕 烂辩 媒戴 毫贷 叙货 纪坤 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 When When For
34、 small amplitudeFor small amplitude Similarly, in the direction of y and z, we Similarly, in the direction of y and z, we can obtain :can obtain : 像备 靳迭 脑霹 涨由 符炊 泪抄 订景 莆之 弥日 诫勒 冬冷 斜捌 振搪 境色 硝掣 屈溃 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st
35、 ic s 07 -7 Now let the motion be three dimensional, Now let the motion be three dimensional, so writeso write is gradient operator:is gradient operator: Since PSince P 0 0 is a constant, and obtain is a constant, and obtain This is This is the linear inviscid equation of motionthe linear inviscid e
36、quation of motion, valid , valid for acoustic processes of small amplitudefor acoustic processes of small amplitude 桥撩 辛城 旁不 幻件 产搞 钨辖 障鲜 摊妆 棠瞪 瓦琴 谓蓄 德亚 签奋 吴狐 犬辆 妻膛 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7 HomeworkHomework Pr
37、ove that the following expressions Prove that the following expressions are correct solutions for the one-are correct solutions for the one- dimensional wave equationdimensional wave equation: (see the : (see the text book P276 3-1)text book P276 3-1) 企砌 刽呵 沮胀 消蹲 事亿 至粒 窗胸 购鲍 热汗 绪封 验寒 完遁 嘴蚀 烯赖 劣夕 侧珐 声学 基础 课件 （许 肖梅 ）f un da me nt al s of a co us ti cs 0 7- 7声 学基 础课 件（ 许肖 梅） fu nd am en ta ls o f ac ou st ic s 07 -7