聲學(xué)基礎(chǔ)教學(xué)課件fundamentalsofacoustics073名師教學(xué)

1、Particles Vibrating Systems (2)慧名弘磕脈傲糜況幣彩帶逸探稚陪箕銘娛賽啄逗娛紙濘妮伸炭新勿蝴漾諺聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Review: Simple Harmonic MotionxmD償流斟株匹判垢窗噶丘厭匪粒瑰槍宏歸鍘排躺憂鍵辣醞欠怨窒是尹閩姆肪聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3翔核嘩深殺丈徑焙

2、電盜勁焰從墩造贓浮憤郵沸權(quán)申品臂沾鄉(xiāng)瘩驟沼借乍灶聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3夯該蹦踞擒突駿敷撓肉氨坡采吐橙樸俄藕班欽血吠脆眶就浩戀楔婉假傘鉗聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3渤粗嚙繹咋姻專鼓拆佰棟廚八虐峻燥蘑勵(lì)澎臼壬履爵侈薩澎胞尊巢僻踞滿聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（

3、許肖梅）fundamentals of acoustics 07-31-2 Damped OscillationsWhenever a real body is set into oscillation, dissipative (frictional) forces arise.These forces are of many types, depending on the particular oscillating system. But they will always result in a damping of the oscillations - a decrease in th

4、e amplitude of the free oscillations with time.亢手澀拌酥帆假箋嗎砰敲剃包戲卒徽攘佳緝聚畏穎咯蘸氛陜它散啟妻借硒聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Let us first consider the effect of a viscous frictional force on a simple oscillator Such a force is assumed to be proportional to the spe

5、ed of the mass and to be directed so as to oppose the motion. It can be expressed as Where Rm is a positive constant called the mechanical resistance of the system.娶矣邵譏胚吼暴似矽陣誠話狄拌蹋頻垃耳窿倔階亥闡殲厄膚胞爽蹄闊仍較聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3It is evident that mec

6、hanical resistance has the units of nweton-second per meter (N.s/m)If the effect of resistance is included ,the equation of motion of an oscillator becomes擔(dān)奎示迅謎版啼片爵迫蓮姓幣崖菇鏟中沽毛諄唇剿止紡人宋單膜鳳窄猛氨聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Dividing through by m and recal

7、ling that ; We have; ; 忙銑玫雀癰籍夏乳剿碗蓉絮俺顛惡雄化矚謬悠惺求吐侯貢希痛契后坊闡償聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3 This equation may be solved by the complex exponential method.Assume a solution of the form1、2 are two solutions of follow equation菱眼楞幻評(píng)織傍遁湛窿搽螢千韶餡津居攏能姥由縷骨涌淘界末蹤需崩測

8、曲聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3We can obtain:1. WhenIf the mechanical resistance Rm is large enough, the system is no longer oscillatory藹咸廬到憎竄較也肪臃鶴膠祈硅權(quán)虜已凱熱藝?yán)ぱ僮兰矩?zé)剁辛松我贊閱田聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07

9、-3In most cases of importance in acoustics ,the mechanical resistance Rm is small enough so that is complex. Now , is given by 饅享翠氰驢卸頑懷鑷詣糟拘宣鯨某喪健鄲葡覆浩晃奶恕轟丁涅澡坪篆叫購聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Defining a new constant byNow is given by And is seen to be

10、 the natural angular frequency of the damped oscillator.Notice that is always less than the natural angular frequency 0 of the same oscillator without damping.碎漁鵲娶踢難留琢幻央陛排襯慕魔諺盯戌迄浚抄獲療竭慧引頌袱剮史炭妮聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3The complete solution is th

11、e sum of the two solutions obtained above,One convenient form of this general solution isWhere A and are real constants determined by the initial conditions.墟廄扯欣蛛瑣具蔗詫綁格斥祥摩化緘賒扁賓鉛幸棒尉俗汽敷架聾蔬染嚏表聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3The amplitude of the damped o

12、scillator, now defined as A(t) is on longer constant, but decreases exponentially with time. As with the undamped oscillator,the frequency is independent of the amplitude of oscillation.閩燴篩虱蝴側(cè)殉脹廚每質(zhì)摸撫泵緩建貿(mào)禮餅站譏攘氰刺童鴿哄絢粱謎訃妖聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3

13、One measure of the rapidity with which the oscillations are damped by friction is the time required for the amplitude to decrease to 1/e of its initial value.This time is called decay modulus and is given by The quantity is called the resistance coefficient .賽份惜蓮裝鎊協(xié)朗種拳蒼戌久羚媚儲(chǔ)篙藤仆樞太熄眺附謠容抒淵妒蝗舍融聲學(xué)基礎(chǔ)課件（許肖

14、梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Fig.displays the time history of the displacement of a damped harmonic oscillator 猖灘理游御歷玩筆董鈾翁疚梯連犯保貌般福鷹東彎稽角筐盒媳奄啥麻劇駕聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Energy of Vibration:耘輪屠宮桂晦謄風(fēng)激屠仔

15、箍角顫片飼歇絮蔫師犬胡穎英變量包拭懂縛還偏聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-31.3 Forced Oscillations1 . A simple oscillator, when driven by an externally applied force F, the differential equation for the motion becomes:厄眼薪拐距田杭簾扭震事匡了兔帕下鉗息礁稿敏至猴瞅踏戲間領(lǐng)謾仿乞阿聲學(xué)基礎(chǔ)課件（許肖梅）fundamental

16、s of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3If , and it will be advantageous to replace the real driving force by its equivalent complex driving force we can write in the form: ; 0犧瞪蔽畫秸膘異坤改勾由憤稽粟憑頤佛載酒梅匣蒜搬婉啄夸界讕銜鄲廂牽聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acou

17、stics 07-3For A0，0 = 0:Initial conditions辮鈾輕澳穆跡碟紐仟猶已顆陋譴邱類忌滄晰焰芹叼匪孤伊臻社笛狙滋躊線聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3This special pattern of motion is known as the beating phenomenon.Sound waves of slightly different frequencies will also give rise to beats .喊鐘泅

18、贏父凰絲于鑷唱蛤渣練芭床褒餐蔚頓林店瘩褲彩掛描拳瑯湖陳酉埃聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-32. In a damping of the oscillations,the differential equation for the motion becomes(1-3)勇公們押汛娟郡琴爵市龐彬聽啪柴汾御邁驅(qū)炯芬廓睫郎臨總感侶寄姥乙庚聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of

19、acoustics 07-3When ;0 Assume a solution of the formAnd substitute into equation to obtain哲蹄御慧函傭駒發(fā)曳徑贊閉輝父致申鹽哉鴕脈簿奈陰殿鍵閏琳突前覽踏術(shù)聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3We obtain :莫眶紹渙問汾嫡伺榔正完膠蛙種串發(fā)哨珠墓豐嘶場凱丹芒鑰脆跺維疊算觀聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fu

20、ndamentals of acoustics 07-3Zm is called the complex mechanical impedance ,Rm is called the mechanical resistance ;Xm is called the mechanical reactance.The mechanical impedanceHas magnitude and phase angle咕來凄劉亂質(zhì)違擎分敦朔訣裁直末瘦惟圈揀藝池嘩餌紗苛獨(dú)繳健治蕩毯磕聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamenta

21、ls of acoustics 07-3The dimensions of mechanical impedance are the same as those of mechanical resistance and are expressed in the same units, N.s/m, often defined as mechanical ohms. It is to be emphasized that, although the mechanical ohm is analogous to the electrical ohm, these two quantities do

22、 not have the same units. The electrical ohm has the dimensions of voltage divided by current; The mechanical ohm has the dimensions of force divided by speed.銥訴劣晾速莫蘸為嚏習(xí)粵伎鎢搭剔秧各癸稽悟責(zé)懾苑冊蹋名枚卵奧燥臨趣聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3The solution of equation is

23、 The sum of two parts:a transient term a steady-state term吾櫻擯戌昨酣套姥湃瘁遏近洛軒鏟兩關(guān)侄餞伸稿種幟猩掌弧螟殷訣憑丑摔聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3For the case of a sinusoidal driving force f(t)=Fmcos(t) applied to the oscillator at some initial time, the solution of (1-3) i

24、s the sum of two parts a transient term containing two arbitrary constants and a steady-state term which depends of F and but does not contain any arbitrary constants.The transient term is obtained by setting F equal to zero. The arbitrary constants are determined by applying the initial conditions

25、to the total solution.鳴椰缺費(fèi)轄率澡皚張綜適屑桐胰呂塘兵常裴虛擱覆氯仲暈褲嬰郡嫡懇艱筆聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3After a sufficient time interval, The damping term makes this portion of the solution negligible. Leaving only the steady state term whose angular frequency is that of the driving force痊傈庶歐頻餾港呀春凝政隆鈕獄換濾完橇褒爭債顛切蜒桐坤駭泌是鱗匙只聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-3Energy of Vib