1、pagepage 1授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineering第第6章章 噪聲控制的聲學基礎(chǔ)噪聲控制的聲學基礎(chǔ)Chapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equation6. 2 Basic Characteristics of Plane Sound Wave6. 3 Acoustic Energy in Sound Field6. 4 S

2、ound Levels6. 5 Radiation of Sound Source6. 6 Sound Field in Roomspagepage 2授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringChapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equationpagepage 3授課人柳貢民2022年5月1日星期日動力與能源工程學院College

3、ofCollege of Power and Energy EngineeringPower and Energy Engineering(1) Sound Pressure（聲壓）（聲壓）A variation in pressure above and below atmospheric pressure is called sound pressure (p), in units of Pascal (Pa) The root-mean square (rms) pressure TedttpTp02)(1Chapter 6 Fundamentals of Acoustics for N

4、oise Control6. 1 The Wave EquationFor harmonic waves, there are2mepp Here pm is the amplitude of sound pressure.pagepage 4授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineering(3) Speed of Sound（聲速）（聲速）The speed of sound is the rate at which a sound

5、wave propagates through a given medium For an ideal gas, the speed of sound is a function of the absolute temperature of the gas RTcChapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave EquationThe acoustic pressure and particle velocity are related by the specific acoustic impedance（聲阻

6、抗率）: (2) Particle Velocity（質(zhì)點振速）（質(zhì)點振速）The acoustic particle velocity (u) is defined as the local motion of particles of fluid as a sound wave passes through the material. upZ pagepage 5授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringChapter 6 F

7、undamentals of Acoustics for Noise Control6. 1 The Wave Equationwhere is the specific heat ratio（比熱比）, R is the specific gas constant（氣體常數(shù)） for the gas, R=287 J/kg-K for air, and T is the absolute temperature of gas in degrees Kelvin, equal to 273.15 plus the temperature in degrees Celsius. The reci

8、procal of the frequency of a pure tone is the period in seconds (4) Frequency and PeriodThe number of pressure variations per second is called the frequency of the sound, in units of Hertz (Hz) 20Hz 20 kHz audible soundsfsound 20kHz called ultrasounds (超聲波)fsound 20Hz called infrasounds (次聲波）Dolphin

9、s and bats can emit ultrasonic waves.pagepage 6授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineering(5) WavelengthWavelength is defined as the distance the pure-tone wave travels during a full periodwavenumber (k) is defined ascTfc22cfckChapter 6 Fu

10、ndamentals of Acoustics for Noise Control6. 1 The Wave EquationFrom this equation we know that high frequency sounds have short wavelengths and low frequency sounds have long wavelengths.pagepage 7授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineerin

11、g推導(dǎo)理想流體媒質(zhì)中的聲波方程的四個基本假設(shè):1）媒質(zhì)為理想流體，不存在粘性，無能量損耗；2）媒質(zhì)是均勻連續(xù)的，無聲擾動時媒質(zhì)在宏觀上處于靜止狀態(tài)；3）聲波傳播過程是絕熱過程，壓強僅是密度的函數(shù)，可以不考慮溫度的因素。因此可以用聲壓、質(zhì)點振速和密度這三個參數(shù)來描述聲場；4）媒質(zhì)中傳播的是小振幅壓力波，各聲學參量都是一階微量，遠小于平衡狀態(tài)的參數(shù)。Chapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equationpagepage 8授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofColl

12、ege of Power and Energy EngineeringPower and Energy EngineeringAcoustic disturbances can usually be regarded as small-amplitude perturbations to an ambient state The momentum equation (movement equation) The mass conservation equation (continuity equation) pPP0uUU000)(Ut0PDtUDFor the quiescent mediu

13、m, neglecting the second-order and higher-order acoustic terms yields the linear acoustic equations 00ut00ptuThe mass conservation equationThe momentum equationChapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equationpagepage 9授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power a

14、nd Energy EngineeringPower and Energy EngineeringThe state equation: The acoustic disturbances in ideal gases are idealized as adiabatic process. The state variables satisfy the isentropicity equation The grouping results from a Taylor-series expansion in and neglecting the second-order and higher-o

15、rder acoustic terms, leads to Submitting the state equation of ideal gases into the speed function of sound wave0000PpP00Pp2cpChapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equation0tanPconstTRP0000PpRT20RTcpagepage 10授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Ener

16、gy EngineeringPower and Energy Engineering00ut 00ptuThe mass conservation equationThe momentum equationThe state equation 2cp012222tpcpThe Wave Equation 2222222zyxThe Laplacin operator for three-dimensional problems is given Chapter 6 Fundamentals of Acoustics for Noise Control6. 1 The Wave Equation

17、pagepage 11授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringThe mass conservation equationThe momentum equationThe state equation The 1-D Wave Equation 00 xut00 xptu2cp01222022tpcxpChapter 6 Fundamentals of Acoustics for Noise Control6. 2 Basic

18、Characteristics of Plane Sound Wavepagepage 12授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringSolutions of the one-dimensional wave equationIf the time dependence is assumed to be the harmonic and the solution of one-dimensional wave equation m

19、ay be expressed as tjexptxp)(),(. 0)()(222xpkdxxpdThe one-dimensional Helmholtz equation The solution of one-dimensional Helmholtz equation may be expressed as a combination of sine and cosine, or complex exponential form as jkxjkxBeAexp)(Chapter 6 Fundamentals of Acoustics for Noise Control6. 2 Bas

20、ic Characteristics of Plane Sound Wavepagepage 13授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineeringrepresents superposition of two progressive waves with amplitudes A and B moving in opposite directions Substituting the solution in the momentum e

21、quation yields )()(),(kxtjkxtjBeAetxp)()(01,kxtjkxtjBeAeztxuSolutions of the one-dimensional wave equationChapter 6 Fundamentals of Acoustics for Noise Control6. 2 Basic Characteristics of Plane Sound Wave1( , )pu x tdtx pagepage 14授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy Eng

22、ineeringPower and Energy EngineeringSubstituting the first term of sound pressure expression into the above expression yields Characteristics of the plane wave sound equationttxxptxp0000,1)(xktjetcx0 , so . It means that the first term of sound pressure expression represents the traveling wave in th

23、e positive x direction.0t0 xtxc0Velocity of sound propagation, or speed of soundThe particle displacement at the position )(000kxtjecjAudt)()(0020tjatjkxjeeecAChapter 6 Fundamentals of Acoustics for Noise Control6. 2 Basic Characteristics of Plane Sound Wave()( , )jt kxp x tAepagepage 15授課人柳貢民2022年5

24、月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringKinetic energy of a volume V01 Acoustic energy and acoustic energy densityPotential energy2001()( )2kEVut10VpVEpdV Total energy22000020002pcVpdpcVEpp2202020012pcuVEEEpkChapter 6 Fundamentals of Acoustics for

25、Noise Control6. 3 Acoustic Energy in Sound Field00VdVdVdVdconsVdcdpcp2020dVVcdp0200pagepage 16授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringThe acoustic energy densityFor the plane traveling waveThe average acoustic energy density2020220021)(

26、cpuVEt)(cos)(cos)(cos21)(220022202022202020kxtcpkxtcpkxtcptaaa1 Acoustic energy and acoustic energy density2002200202)(1cpcpdttTeaTChapter 6 Fundamentals of Acoustics for Noise Control6. 3 Acoustic Energy in Sound Fieldpagepage 17授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy Engin

27、eeringPower and Energy EngineeringThe acoustic energy radiated by a sound source per unit time is called sound power, denoted as W and the unit is the watt (W). Sound intensity is defined as a measure of the acoustic energy passing through a unit area perpendicular to the direction in which the wave

28、 is traveling per unit, denoted as I and the unit is . 2 Sound power and sound intensity2/ mW0( )WI tcSChapter 6 Fundamentals of Acoustics for Noise Control6. 3 Acoustic Energy in Sound Field0Wc S)()()(tutptI聲強的定義式pagepage 18授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy Engineerin

29、gPower and Energy EngineeringThe average sound intensity2 Sound power and sound intensitydttutpTdttutpTITT00)(Re)(Re1)()(1SIdsWChapter 6 Fundamentals of Acoustics for Noise Control6. 3 Acoustic Energy in Sound Fieldpagepage 19授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy Engineeri

30、ngPower and Energy EngineeringThe relationship between sound intensity and average sound energy density3 Sound power and sound intensity for plane sound waveFor the plane sound wave traveling in the positive x direction2002apIc2aepp 2aeuu where and are the effective sound pressure and particle veloc

31、ities, respectively.0cI Chapter 6 Fundamentals of Acoustics for Noise Control6. 3 Acoustic Energy in Sound Field2002cpe200epc20 012ac u20 0ec u12aap ueep upagepage 20授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringAnother reason is that the hum

32、an ear hears logarithmically, that is, it judges the relative loudness of sounds according to the ratio of their pressure. The important thing to remember about the decibel is that it represents a relative measurement, or ratio. A healthy human ear can detect pressures as low as about 20 Pa, compare

33、d to the normal atmosphere pressure (1.013x105 Pa) around which is varies, a fractional variation of 2x10-10. Amazingly, the ear can tolerate sound pressures up to more than one million times higher.In order to compress the large range of typical sound pressures into a smaller, more understandable s

34、cale, the sound levels are described on a logarithmic scale in units called decibels (dB). Chapter 6 Fundamentals of Acoustics for Noise Control6. 4 Sound Levelspagepage 21授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringSound Pressure Levelwher

35、e is the standard reference pressure in air. refpppLlg205202 10refpPaPaSound Power LevelrefWWWLlg101210refWwhere (W) is the standard reference sound powerSound Intensity LevelrefIIILlg10where (W/m2) is the standard reference sound intensity1210refIChapter 6 Fundamentals of Acoustics for Noise Contro

36、l6. 4 Sound Levelspagepage 22授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringChapter 6 Fundamentals of Acoustics for Noise Control6. 4 Sound Levels關(guān)于聲壓級的一些典型例子：人耳剛剛能聽到的聲音:至分貝；手表聲、落葉的沙沙聲：分貝；兩人的輕聲耳語：分貝；一般居室里的聲音：0分貝；公共汽車的響聲、鬧市區(qū)的聲音：80至90分貝；織布車間：不低于

37、100分貝；噴氣式飛機的聲音：約140分貝。一般認為超過60分貝的聲音是噪聲。pagepage 23授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineeringpagepage 24授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringHome WorksPage 195Page 195Quest

38、ions: 7-1、7-2Chapter 6 Fundamentals of Acoustics for Noise Controlpagepage 25授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineering波陣面保持為S不變的波動方程為rP22222021()pprprrrctChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Source

39、222220ln1ppSprrrct對于球面波， S=4r2代入上式后方程化為0)(1)(222022trpcrrppagepage 26授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringrP)()(),(krtjkrtjerBerAtrp( , )jtkrAp r terChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound SourceC

40、onsider only waves moving radially outward from the source or the case for no waves reflected back toward the origin, we must have B=0 0)(1)(222022trpcrrpFor spherical sound field, the wave equation is Solution of the wave equation of spherical sound wave ispagepage 27授課人柳貢民2022年5月1日星期日動力與能源工程學院Coll

41、ege ofCollege of Power and Energy EngineeringPower and Energy EngineeringIntegrating the momentum equation leads to the expression of particle velocity The specific acoustic impedance krtjejkrrAjdtrtrptru11),(1),(000 01jSSjc krpZZ eujkr2/122001rkkrcZSkr1tanThe magnitude of the spherical acoustic imp

42、edance is The phase angle between the acoustic pressure and particle velocity is Chapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Sourcepagepage 28授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringThe constant A in p(r

43、,t) and u(r,t) may be determined, by assuming the vibration velocity at the sphere surface is known asConsider , and denoting (the source strength) The average sound intensityThe sound power radiated from the sound source au20 01ajc ka uAjkar=+1ka24aQa u004jc kQArp=222200032)Re()Re(1rQkcdtupTIT84220

44、02QkcIrSIWChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Source()()001( , )(1)jtkajtkaaAu a tu eec ajkawwr-=+pagepage 29授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringThe sound pressure may be expressed asThe effe

45、ctive sound pressureThe relation between sound intensity and sound pressure2/004),(krtjerkQctrp00242aepc kQpr002cpIeChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Source( , )jtkrAp r terjkaukacjAa1200It is the same as in plane sound fields.pagepage 30授課人柳貢民2022年5月1日星期日動

46、力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineering12( )10lg10I rSILChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Source12212104lg1010)(lg10rWrISIL21210lg10lg10lg410WrFor a spherical sound field, the relationship between the sound inte

47、nsity level and sound power level may be established as below.25 25 2120 0(2 10 )10lg10lg(2 10 )10epc2120 010lg10epc25252120 0(2 10 )10lg(2 10 )10epc0 040010lgSPLc20lg11SWLrpagepage 31授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineeringso for the a

48、ir medium at room temperature, which leads to The sound pressure level lowers 6 dB if the distance is doubled. 00400lg10cSPLSIL4153432 . 100cSPLSILChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound SourceBecause 2211120lg1120lg20lg2 11(20lg11)66rrSILSWLrSWLrSWLrSIL16. 0400l

49、g1000cLets consider the value of SIL ,if r=r2=2r1,then from the equation above ,we may get pagepage 32授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy EngineeringDipole source:Two closed small oscillating sphere sources with same vibration amplitude and op

50、posite phase12()()12( , )jtkrjtkrAAp r teerrSound pressure radiated from the dipole source may be expressed as:Chapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Sourcer1rr2lPIf is much less than r ,then one may getlr1cos2lrr2cos2lrrpagepage 33授課人柳貢民2022年5月1日星期日動力與能源工程學院Col

51、lege ofCollege of Power and Energy EngineeringPower and Energy EngineeringChapter 6 Fundamentals of Acoustics for Noise Control6. 5 Radiation of Sound Sourcecoscos()22klkljjjt krApeeer()cos2 sin2jt krAklejrSoConsider , 1kl coscossin22klkll that means 2klkSo we have()cosjt krAklpjer pagepage 34授課人柳貢民2022年5月1日星期日動力與能源工程學院College ofCollege of Power and Energy EngineeringPower and Energy Engineeringr1rr2lPSound pressure radiated from the dipole source in the far field is lowered as the distance increasing, and is dependent on the angle.Defining of Directivity Charact