Phys 107 Sound Physics Day 6 Ch 3, pt 2 1

Transcription

1 Phys 107 Soud Physics Day 6 Ch 3, pt 2 1 Tu. 1/22: Ch 3 Sources o Soud Th. 1/24: Ch 3 Sources o Soud Tu. 1/29: Ch 4 Soud Propagatio Th. 1/31: Ch 4 Soud Propagatio HW3: Ch3: 2, 3 W, 7 W Ch3: 8 W,9 W Project 1 HW4: Ch 4: 1,3,4, Project Ch 4: 8 W,10 W,11 W, 13 Mo. 1/21 or Tues. 1/22: Lab 3 Strig Istrumets: Vibratig Strig(7.4, 10.1) Mo. 1/28 or Tues. 1/29: Lab 4 Wid Istrumets: Vibratig Air (11.3, 12.1) Materials Toy Guitar o Pick ad bow Wae tak o taper ad log bar ad projector Music box Violi shaped plate o Pasco Drier, uctio geerator (set aroud Hz), sad shaker, ad box lid (like paper reams come i) to catch the sad Computer set or PhET waes o strig(ree ed) Circular plate o Agai, Pasco Drier, uctio geerator (set aroud Hz) ad sad This week s lab equipmet hadout Torsio bars Variable legth Orga pipe Metal Orga Pipe Recorder (the plastic musical istrumet) Hagig Sliky Symbol or ice big pot lid Last Time: bega Chapter 3 Sources o Soud The commo elemets o makig musical souds Commo to all musical istrumets are three importat steps i producig music. o 1) The a-toal impetus o motio, the strike, pluck, or blow o 2) Tuig the o-musical ibratio ito speciic requecies o 3) Ampliyig the motio or creatig louder soud. 2) Tuig Last time, we ocused o how a istrumet tues takes the a-musical impetus ad produces a musical soud. Geerally, that relates to resoace that, gie the geometry ad material o the istrumet it will ibrate at oly speciic requecies. Strig istrumet. More speciically, we cosidered striged istrumets ad how the waerot rom a pluck ca speed dow the strig, relect o its ixed eds, speed 1

2 Phys 107 Soud Physics Day 6 Ch 3, pt 2 2 back ad orth, all alog itererig with its relectios to produce a stadig wae which its o the strig. We did t rigorously walk through the whole process, but hopeully made it plausible. We got quatitatie about the requecies that could be produced by a strig by usig the geeral relatioship betwee requecy, waelegth, ad wae speed or ay wae ad the relatioship betwee wae speed, tesio, ad mass desity speciic to a wae o a strig: T Ad by obserig that the oly simple waes that it o a legth o strig hae waelegths = 2L/ where = 1, 2, 3, Puttig these two together gies us the amily o requecies o 2L T, = 1, 2, 3, harmoic series Striged Istrumets o Last time I spoke geerally about strigs, ow let s thik more speciically about striged istrumets. We ll see that each parameter o the right had side o this equatio gets addressed whe buildig, tuig, ad playig a striged istrumet. Demo: Toy Guitar o Settig requecy respose Costructio Mass desity ( ) - Dieret strigs o dieret mass desities ad thus wae speeds Tuig Tesio (T) wae speeds Playig Legth (L) igerig wae legths Harmoic () playig harmoics is getly placig a iger o a strig where you wat a ode to be, but ot clampig it dow so hard as to preet the whole strig rom supportig the stadig wae. Locatio & type o impetus (strike, bow ) Whe a strig is played, the udametal requecy ibratio domiates, but all other harmoics are also excited ad heard aitly, giig color, or timbre, to the ote that s played. More subtly, the player ca iluece this timbre / how strogly the dieret harmoics are excited / heard by aryig the attack / impetus. Type o Pluck-quick particularly excites high-requecy harmoics 2

3 Phys 107 Soud Physics Day 6 Ch 3, pt 2 3 o Strike slower release dampes out highrequecy harmoics o Bow periodic release as the strig ibrates back ad orth, it s caught ad released by the bow. Locatio whereer you drie the strig, you ehace harmoics with ati-odes there / reduce oes with odes there This Time Mechaical Ampliicatio o Startig at our ear drum, we ca trace the soud back to the source ad see how it ca chage to make the soud louder i our ears. The harder air pushes ito our eardrum, the louder we perceie the soud to be. Thus the air just outside our ear must be gettig pushed hard. Tracig back, the air at the source must be gettig pushed hard. Amplitude o the source s motio. Necessity to moe a lot o air. But i the source is moig terribly ioletly i acuum, as we heard with the bell i the bell jar (or rather ot heard) o soud gets trasmitted. So it s ot just a matter o how much the object, say, guitar strig, moes but how much air it kocks aroud as a result. To push more air, the source should be bigger. Source Size. Demo: Wae tak o First wiggle water with just a iger o The wiggle water with the whole beam same amplitude o motio, but hittig more water bigger waes. Soudig Board. Strig istrumets hae a real problem - Strigs are small, ad so do t bump ito a lot o air, but they ca be achored to somethig that is much larger, whe the strig ibrates, it drags this somethig, soudig board, with it. It s the bridge, ot the hole: there s a commo miscoceptio that the hole i a guitar is where the soud gets i or out the hole itsel is o secodary cocer; the primary commuicator is the bridge the strigs yak back ad orth o the bridge as they ibrate, ad that trasmits the ibratio to the rot plate (ad through a post i iolis, the back plate.) Demo: Similarly, this music box is t ery loud o its ow just the metal ties ibrate, ad the metal body a little, but it s much louder whe achored to somethig big like the table ow the 3

4 Phys 107 Soud Physics Day 6 Ch 3, pt 2 4 table top is ibratig too, ad that pushes aroud a lot more air louder soud. Resoace board / caity colors soud. But the table does t just ampliy the soud, because it too, like the ties themseles, has requecies at which it aturally resoates, so it teds to respod particularly well whe drie at those requecies ad ot so well whe drie at other requecies. Demo: play music box o table, woode box, wall, chalkboard, ad ootboard where chalkboards hide. Visualizig resoace board motio. Demo: ioli back o The dust gathers where the plate is t jumpig so much at the odes. our ioli-back plate has ice resoaces aroud 90 hz 300 hz Now, the resoaces o a complicated shape like a ioli back are, well, complicated. Let s cosider somethig simpler, like a ice roud drum head. 3.1 Percussio Istrumets This brigs us to percussio istrumets their tuig elemets are these 2-D boards. But beig 2-D istead o 1-D, they hae much more reedom about how they wiggle, ad a more complicated relatioship betwee the dieret requecies at which they ca wiggle which is to blame/thak or their ot geerally soudig so musical as strig or wid istrumets. o Drum A drum head is achored all aroud its edges, much like a strig is achored at its edges. So, you ca imagie what some o the simple modes o oscillatio might look like: See Pg. 165 ad 166 o your text o Demo: (select display 2D+3D) o udaetal the middle bows i ad out o 1 st harmoic the two sides slosh up ad dow o cut ito quarters, cut ito sixths, o cocetric rigs, o Demo: circular resoace plate o This is more like a symbol tha a drum head i both material (metal) ad that it s rim is ree to lop. Dieret boudary coditios ree ed. o Now, i cotrast to the drum head, a symbol is ree at both eds. At irst blush, that might make you thik that there are o boudary coditios ad ay old wae-legth oscillatio could be supported. But that s ot the case, ad this is a importat poit ot oly or symbols, but or may wid istrumets, so we ll deelop this careully. o Demo: Pulse relected o ree ed torsio bar, PhET wae-o-astrig This time the mass o the let ed does t hae a buddy holdig it back whe the wae comes rom the right. So it moes extra easily, extra high. The wae pulse is relected right back, right-side-up. 4

5 Phys 107 Soud Physics Day 6 Ch 3, pt 2 5 o Demo: Stadig wae with ree eds (drie i the middle) Try to drie a ew dieret requecies. This is like a cross-sectioal iew o a disc o Like a strig with ixed eds, this oe, with ree eds ca support a amily o waelegths, this time, they must satisy the coditio that there are ati-odes at the eds. o This too gies a simple, iteger relatioship betwee the wae-legths, ad thereore the requecies that ca be supported o 2-D surace oscillatios o So, the symbol ca support a ery similar amily o ibratios to a drum head they re just ati-odes istead o odes at the edges. Voltage aroud 0.6 V; First ew are i rage o 350 to 900 Hz, step by 10 Hz (whe you id you re close to a mode, you ca switch dow to 1Hz resolutio to zero i.) o Impetus Strike At irst blush, the strike eorces o particular requecy, allowig the drum or cymbal to ibrate at its whole amily o requecies; howeer, there is a little selectiity. Stick s. mallet Sometimes a hard headed stick is used, sometimes a sot mallet. This is similar to the dierece i pluckig a guitar strig with a pick s. hittig it with a elt coered hammer as i a piao. The larger ad soter texture adsorbs some o the higher-requecy / shorter-waelegth ibratios dampes them out. This leaes a soud that is domiated by the low requecies. Not as bright. o Frequecy Selectio A drum head is ixed at both eds, so its wae must it the coditio o odes at the eds, like a strig with ixed eds. Costructio Radius: The drum head s radius plays a similar role to a strig s legth i selectig the requecies, so bigger drum heads ca produce deeper toes. Stiess: Chagig the material ad its thickess chages its elasticity / stiess like chagig the tesio i a strig Mass desity: Agai chagig material ad thickess. Tuig Tesio Oe ca adjust the tesio o the drum head 5

6 Phys 107 Soud Physics Day 6 Ch 3, pt 2 6 Playig Locatio o strike Where you strike it is guarateed to be a ati-ode / ot to be a ode. Look at the patters we oud. See which oes ca all agree o a ode or ati-ode locatio. o Ex. Strike i the middle, ad get less respose rom ay thig that has a ati-ode through it. o Strike ear the ar edge ad get a lot o high requecy patters. o Ampliicatio The cymbal or drumhead is already quite large. It eeds ery little help pushig the air aroud. o Additioal Tuig o This alls uder the headig o tuig doe durig the desig ad costructio o a istrumet, but I waited to metio it because it leads ito wid istrumets. o The drum head is typically suspeded oer a hollow cylider. I some istrumets that cylider is ope ad i other it is closed (ex. Timpai). The air i that caity is aother medium which ca ibrate. I the extreme o a xylophoe, the air i the pipe below the bar has its ow atural requecy. I the case o the kettle drum there is some resoace eect, but also the air proides a cushio dampes out some higher requecies. o The role o air iside a istrumet brigs us to the wids. o Not exactly harmoics Now, sice a drum has a lot more reedom to oscillate, all those do t happe to be members o a simple harmoic series, some o them are close, some o them are ot so close. So it s ot so musical soudig as, say, pluckig a strig. Still measures ca be take to select the souds that it produces o Membrae thickess. aryig the thickess o the membrae lowerig the requecies that moe these locatios a lot / raisig the requecies that bed these locatios a lot. o Resoace caity. Moutig resoatig caities beeath like a kettle drum s to emphasize particular requecies. o Locatio o hit. Strikig i particular locatios to excite particular ibratios 3.2 Wid Istrumets The commo elemet is a resoace tube. The actie elemet here is actually the colum o air cotaied iside. This plays a aalogous role to that o the strig i the striged istrumet. Air Colum Wae speed: The speed o a wae i air is determied by the air s properties (Temperature, that it is air ater all, ad ot Helium), i particular, the geeral 6

7 Phys 107 Soud Physics Day 6 Ch 3, pt 2 7 expressio shows the same kid o iterplay betwee iertia ad some sort o kt restorig restorig orce as we saw or waes o a strig: ; while m iertia it s ice to see that old theme playig out i this equatio, gie the temperatures that we ll be iterested i, a more useul approximatio is m s 344 m s T 20 C C Waelegth. We will see that the legth o a colum o air also determies the waelegths that it ca support. Harmoics. These correspod to a harmoic series o requecies. Stadig waes i air o You e see stadig waes o a strig ad see eidece o stadig waes o a surace like a drum head. But what about i air? o Soud wae pressure, desity, displacemet wae. A soud wae is characterized by a ew simultaeous distortios i the air. There is series o pushes that get passed through the air pressure distortios. I respose the air moes displacemet. The air moes to buch up or spread out desity distortios. The easiest or us to thik about ow is the displacemet o the air. Whe a soud wae rot passes through, some o the air molecules get pushed ahead ito their eighbors, they the get pushed back by those eighbors. o Demo: Compressio pulse i a sliky Boudary coditio ope at both eds. Some istrumets are pretty ope at both eds the lute ad some orga pipes. Now, oe might woder what s so dieret about the air i the istrumet s. the air outside the istrumet? The importat dierece is that the air iside is more coied. Imagie stadig outside ad clappig oce; the soud pulse o that clap would radiate out i all directios, but i you clap at the ed o a tube, the soud ca oly trael dow the tube. Whe it gets to the ed, it ca ially spread out. That chage rom beig coied to propagate i 1-D to beig able to radiatig out is eough to cause a relectio. A ope ed o the istrumet will ecessarily be were the air is reest to displace a displacemet ati-ode. The a amiliar lie o reasoig tells us that there is a harmoic series o air waes that ca be supported i the tube. o Demo: ope Orga Pipe, lute. o Oerblowig will excite 2 d harmoic Just as or a strig that s achored at both eds, the ope-eded tube supports waes that it, hae a iteger umber o hal waelegths alog the legth o the tube: L,2, ca play are 2L ad the correspodig requecies that it ca support, otes it 2L where = 1,2,3, 7

8 Phys 107 Soud Physics Day 6 Ch 3, pt 2 8 o Boudary coditio ope at oe ed. The agai, most wid istrumets hae a big gapig hole oly at oe ed. So that ed s has a ati-ode o displacemet (air moes the most) while the other ed has a ode. o Demo: orga pipe with ar ed closed, clariet. Now the waes that it are those that hae a odd iteger umber o quarter waelegths. L,3,... ad so 4 4 where = 1,3,5, Qualitatie Diereces. There are two udametal ramiicatios o this dierece: Whe playig a gie ote, a tube that s ope at oe ed will also excite all o its harmoics (both ee ad odd) while a tube ope at just oe ed will excite oly hal the harmoics (odd) ad so soud thier. to play the same ote, a tube that s ope at both eds must be twice as log as a tube that s ope at just oe ed. Because the oe tube eed oly be as log as a quarter o the soud s waelegth while the other would eed to be hal the waelegth log. We ca see this mathematically o L oe ed oe ed ope ope both eds ope both eds ope 2L 2L both eds ope oe ed ope More about resoatig air colums i lab ext week. Example: (like homework) *Let's thik about that ariable-legth orga pipe I had; you probably could't see, but alog oe side o the slide were markig idicatig how ar it should be pulled out to play dieret otes. Say pullig it out 0.39m allowed me to play A4 (440 Hz); the i I pulled it out 0.44m, what ote would it play? I kow that or this orga pipe the udametal it plays relates to its legth ia Writig that or both cases, A?? A 8

9 Phys 107 Soud Physics Day 6 Ch 3, pt 2 9 I ca diide the two equatios by each other, or equiilatly, sole both or /4 ad the set them equal to each other (sice the wae speed will be the same i both scearios) LA 0.39m ALA? L?? A 440 Hz 390 Hz L 0.44m 4? which, the iside back coer o the book says correspods to G4 (at least to two sigiicat digits). o Note: i the ed, it we did t make use o the alue o or that it was diided by 4. A similar problem askig about waes o a strig o dieret legths would hae played out exactly the same. Fairly geerally or a wid or strig istrumet, the requecy scales iersely with the legth, or, comparig two requecies ad correspodig legths L o 1 1 2L2 Impetus o While a sigle pluck sets a strig ibratig or a while, a sigle blow is t quite so eectie, you eed a cotiuous blow, ad kid o like the cotiuous draw o a bow across a sprig quickly sets up a stick-slip behaior i sych with the strig, the cotiuous blow gets reshaped ito a serious o pus i sych with the ibratig air. o Edge Toe. Oe way to get this is with a edge toe - we get this thaks to air turbulece aroud a edge, say aroud a reed or the edge i a lute hole or a orga pipe. I some o these cases, the requecies produced are airly speciic, soudig a little like a duck call ot too musical, but deiitely has a basic pitch. o Demo recorder Tuig& Ampliicatio o Resoace betwee air colum ad impetus. I either case, this air motio cotais requecies i the air colum s harmoic series (alog with lots o requecies that are t i the series). Those requecies that it are reiorced as stadig waes i the air resoate ad grow. Those requecies o motio are ampliied. I some istrumet, the pulsig o air that is set-up comes back to the poit o impetus (say the buzzig lips o a brass, or the reed o a wood-wid) ad reiorce its motio at the right requecies. o Playig. o Chage legth. A tromboe is the easiest to cosider you literally legthe or shorte the resoace tube, thus icreasig / decreasig the waelegth ad lowerig or raisig the correspodig pitch. o Chage driig requecy. Aother strategy is chagig the basic requecy at which your driig the system, say pursig your lips harder sice the colum legth remais the same, all you ca hope to do is jump rom driig rom oe to aother resoace jump octaes. 9

10 Phys 107 Soud Physics Day 6 Ch 3, pt 2 10 o Eectiely chagig legth. Some istrumets hae ery large holes, ad whe you ucoer them you eectiely chage the legth o the istrumet. o Select harmoics. Others hae small holes, still, opeig them allows their locatios to be pressure ati-odes, ad so selects the requecy at which it plays. o The bell eect. Most istrumets hae a laired bell at the ed, rather tha a abrupt stop; oe eect o this is that the boudary coditios is a little lexible there must be a atiode somewhere i the bell, but you ca push it. 10