Physics for Audio Engineering
Physics for Audio Engineering PHY 2010
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This 6 page Class Notes was uploaded by Werner Hagenes on Saturday October 3, 2015. The Class Notes belongs to PHY 2010 at Belmont University taught by Scott Hawley in Fall. Since its upload, it has received 36 views. For similar materials see /class/217964/phy-2010-belmont-university in Physics 2 at Belmont University.
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Date Created: 10/03/15
Reiieiheiatioii Detail chapIEIL Everest uaiequaiitiesara raarh 39m and N01sz Modes p uSihg Sinewzveszt iawrrequeheies aherihas arthe raarh grig 2m iahger n at variuus 771 a iryau mezsureT frequencies Currespuridirg ta harrhai made 3 kHz inkiiz 3W 1W Fi une Cy r H 1 kHz 7 eratiaii time measured with pure siiie signals at law ireqiieiicies ieveais slnvl sounii aetay lung revemeiatioii time at the modal irequeiicies niese peaks apply Duly i r modes an a iiie n the mall as a whale High madaldenr resuitiiigiii uniformity ofdis rihution 0f snund eneigy aiiii randomizing nfdirecr l mpaganon is netessary far IEVelbelali ll equations to apply ineraiiew and h the graph are hat representative uf the average praperties uf the ufzsing erwerberztiuntimeufz umes r The peaksi raarh e high maaai density 1 L tsufmudesnezrezchutherinfrequency 2 Cunsequencesuf high maaai density a Unit mdislribul Rahaarhaireaiaharprapagatiah b You don t get high modal density for a small room below 500 HZ W or higher Thus people rarely speak of a quotreverberation time for a small room Instead you may hear of a quotdecay rate eg 20 dB per second 3 Measuring Reverb Time a Lets revisit the sound arriving at a listener as a function of time b bunch of crap I didn t type here 4 Mode decay variations a Reasons why its harder to get reverb times for low frequencies than high P frequencies 39 Harder to make loud for low frequency noises ii Often noise floor is higher at low frequencies AC units Seismic noise iii Mode decay variations can make fitting a line to the decay more difficult than for highs iv Low frequencies tend to imply lower modal density 1 Density how close the modes are together 5 Modal Decay Variations If you record multiple decays you ll find that they look similar but the quotwigglesquot are a different for each one This is a bigger effect a low frequencies than high When you cut off the random sound sources at the moment a particular set of modes were excited This set is different each time you record a new decay Because source is random b Typical Measurement Procedure i 3 mic positions ii 5 decays per position iii 8 octave bands per decay 1 eg centered around 63 Hz 125 Hz 250 Hz 500 Hz 1 KHZ 2KHZ 4 KHZ 8 KHZ This is done by filtering the decay into different octave bands This Iquot also helps with signal to noise ratio c Frequency Effect i Wiggles in the decay rate will be larger with lower frequencies High frequencies have smaller wiggles d Acoustically Coupled Spaces i Acoustically coupled spaces 1 eg a concert hall with doors open to a marblelined atrium e Electro acoustically coupled spaces Sound is recorded in one room with some reverberation time TR Then is played back in another room with different reverberation time or even the same room iii In general The reverberation time of the listening room should be a little more than the reverberation time of the recording room iv The total reverb time is a little longer but close to which ever reverberation time is longer for some room total TR 20 more than original TR 1 2 3 Absorption chapter 9 Everest Dissipation of Sound Energy a quotConservation of Energy Energy Can t be created or destroyed by can be changed into different forms Sound energy is in the form of motion of Air Molecules Kinetic Energy This can be dissipated by converting it into heat or thermal energy ie uncorrelated motion of air or other particles anda electromagnetic radiation infrared Absorption of Air a Frequency b 1Khz c 2KHZ d 4Khz ASabins per 1000ft3 09 23 72 Types of Absorbers a Porous and Resonant Porous 1 Rely on sound penetrating quotintersticesquot of material and causing material to move Frictional losses in this motion result in dissipation of energy as heat ie sound does work on something that something dissipates energy as heat 2 Porous absorbers are often fuzzy or quotfoamyquot Density and thickness effect the amount of absorption 1 Thickness has more of an effect on low frequencies than in high 2 Density also affects which and how many frequencies are absorbed a quotToo dense Sound may just reflect off resulting in poor absorption 3 Not dense enough sound will be quottransmitted and not be affected by the absorber b Say you have a piece of porous absorber and a sound of intensity Ii is incident on it Some of the sound will be reflected with intensity TR Some transmitted IT and some absorbed 5 vii Ii IR IT IA I R reflection T transmitted coefficient A energy absorption coefficient lRli lT li The energy absorption coefficient 01 01 l R The energy absorption coefficient 01 is 01 l R Frami39uri of energy nut re ected and Sabine absurpti39un coef cient a i39sgi39veri by 2 enuee a SL7qu pressure i39s maximum in carriers z i b Where feisthe frequmcylu which thesy nlsmned Table 114 SoLnd decay in vesorant absurhers Reverberation umquot secon is 22 011 100 H022 OIKE iiie Inning curve of a iieimimiiz type iesmiam ibsnrber has been dllelnlined its Man can be found mm me expiessinn fuAf The revelbualion limequot uf sum absomen is very simn m 115 normally enmumered oisound E ectiun ebsurpuum and aimsmn arethree primary pruness m mum acuuslics b PradiczHy speak n Cid m Hg apsuigveresi dffusersczn heip mmmi mum mudesznd u n c withuutSgnificzntiyaffeairgreverbtimes zysdech39e 39ng i u Bui on EU nut at right 2 A z ngies we ise bad diffuser v Diffrzaiungrzdirg Re ectiunphzsegr2ding diffusers s phesegmig chmEdEl m 2 Am SE radiungrztirg ise 5m uf bumpsurbzrswhich scatters away in avariety uf irectiuns b Differentgrztingshzve been used in upticsfuravery iungume i Butter y Wings smny Cuiured aeeiies P 5quot For some directions you get constructive interference and for other you get constructive interference and for others you get destructive interference The scattering is greatest when quotdquot and quothquot are comparable to the wavelength A A typical grating will tend to scatter one wavelength frequency range more than others Which may is not desirable for good room acoustics By varying the spacing d and height h and even making the spacing differing from the width w of each bar we can affect a wide range offrequencies A random sequence of bars of different height can work well for something or diffusing a range of frequencies Construction wise its convienient to keep d and w the same very h eg to use a stack of wooden boards ofthe same thickness The height h places a limit on the frequencies that are scattered because h M4 is the limit of 180 degree phase difference between incident and reflected sound at normal incidence The use of pseudo random sequences in different gratings was applied by Schroeder in the late 70s and early 805 These sequences are based on the idea ofa remainder or modulus i Popular example 1 Quadratic Residue 2 quotWell Depth h n2 mod p 3 Where p is some prime number a number that can only be divided by itselfand one 4 Say P 5 N Hn mod 5
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