Chapter(11

1 Chapter(11 Vibrations*and*WavesDamped'Harmonic'Moti onIn#simple#harmonic# motion ,#an#object#o scillates#with#a#constant# #reality,#friction#or#some#other#energy# dissipating#mechanism#is#always#present# and#the#amplitude#decreases#as#time# #is#referred#to#as#damped'harmonic' 'Harmonic'Motion1)simple)harmonic) motion ) amplitude)stays)constant2&3)underdamped amplitude)decreases)but)still)oscillatio ns4)critically)damped) amplitude)decreases)to)0)without)oscilla tions)inshortest)possible)time5)Overdamp ed amplitude)decreases)to)0)without)oscilla tions)slowerthan)in)critically)damped)ca seDifferent(types(of(damped(harmonic(mot ion:Driven'Harmonic' motion 'and' ,. ,.f0,. 1 of 1 Stickies3/30/14, 12:15 AMf0=12 kmThe$Nature$of$ $wave$is$a$traveling$ $wave$carries$energy$from$place$to$ $Nature$of$WavesLongitudinal$Wave$5the$ disturbance caused$by$the$wave$moves$along&the$direc tion$that$the$wave$propagates,$ ,$sound$waves,$ compressed$slinky$waves.

2 The$Nature$of$WavesTransverse$Wave$0the$ disturbance caused$by$the$wave$movesperpendicular+to +the$direction$that$the$wave$propagates, ,$water$waves,$ shaken$slinky$waves fTv==Since&velocity&isdistance/time&&&&& &&&&!The&propagation&velocity&of&a&perio dic&wave&is&related&to&its&frequency& :&Periodic(WavesExample:The$Wavelengths$ of$Radio$WavesAM#and#FM#radio#waves#are# transverse#waves#consisting#of#electric# andmagnetic#field#disturbances#traveling #at#a#speed#of# ##A#stationbroadcasts#AM#radio#waves#who se#frequency#is#1230x103Hz#and#an#FM#rad io#wave#whose#frequency#is# ##Find#the#distance#between#adjacent#cre sts#in#each#wave.!!fTv==fv=!Periodic(Wav esAMm !!==fv"FMm !!==fv"The$Speed$of$a$Wave$on$a$StringTh e$speed$at$which$the$wave$moves$to$the$r ight$depends$on$how$quicklyone$particle$ of$the$string$is$accelerated$upward$in$r esponse$to$the$net$pulling$ $densityThe$Speed$of$a$Wave$on$a$StringE xample:$$Waves&Traveling&on&Guitar&Strin gsTransverse(waves(travel(on(each(string (of(an(electric(guitar(after(thestring(i s(plucked.)))))))))))))))

3 ((The(length(of(each(string(between(its( two(fixed(endsis( (m,(and(the(mass(is( (g(for(the(highest(pitched(E(string( (g(for(the(lowest(pitched(E(string.((Eac h(string(is(under(a(tension(of(226(N.((F ind(the(speeds(of(the(waves(on(the(two( $Speed$of$a$Wave$on$a$StringHigh%E()()sm 826m 2263-=!==LmFvLow%E()()sm207m 2263-=!==LmFvThe$Speed$of$a$Wave$on$a$St ringConceptual$Example:$$Wave%Speed%Vers us%Particle%SpeedIs#the#speed#of#a#trans verse#wave#on#a#string#the#same#as#the#s peed#at#which#a#particle#on#the#string#m oves?Speed%of%longitudinal%wavesLIQUIDSS OLID(BARSv=B B bulk modulusv=Y Y Young's modulusExample:Compare(the(speed(of(a(wa ve(in(water(to(a(wave(in(a(bar( :Aluminum:B= 109 N/m2 =1000 kg/m3v=B = 1091000=1500 m/sY= 1010 N/m2 =2700 kg/m3v=Y = 10102700=5100 m/sIntensityWaves&carry&energy&that&can& be&used&to&do& ,is&defined&as&the&power&that&passes&per pendicularly&through&a&surface&divided&b y&the&area&of&that& ://Sound&Intensities12x10%5W(of(sound(po wer(passed(through(the(surfaces(labeled( 1(and(2.)))))))))))))))))))))))))))))))) )))))))))))))))))))))))))))))))))))))))) ))))))))

4 ((Theareas(of(these(surfaces(are( (m2and(12(m2.((Determine(the(sound(inten sityat(each( !!"="== !!"="==APII ntensity24rPI!=power&of&wave&sourcearea& of&sphereIf&the&source&emits&the&wave&un iformly*in*all*directions,*the&intensity &dependson&the&distance&from&the&source& in&a&simple& r2 I 1r2 I1I2=r22r12 For SHM E=12kA2 I P E A2 I1I2=r22r12=A12A22 r2r1=A1A2 Example:)The$intensity$of$an$earthquake$ wave$passing$through$the$Earth$is$measur ed$to$be$ 106J/(m2s)$at$a$distance$of$44$km$from$t he$ $was$its$intensity$when$it$passed$a$poin t$only$ $km$from$the$source?At$what$rate$did$ene rgy$pass$through$an$area$of$ $m2at$ $km?I1I2=r22r12 I1=I2r22r12= 106()44212= 109 J/(m2s)P=I1A1= 109() ()= 1010 J/sWave%Fronts%and%RaysDefining'wave'fro nts'and' )a)sound)wave)since)itis)easier)to) )is)a)hemispherical)view)of)a)sound)wave )emitted)by)a)pulsating) )raysare)perpendicularto'the'wave'fronts ( )crests))which)are)separated)from)each)o ther)by)the)wavelength)of)the)wave,)!

5 Wave%Fronts%and%RaysThe$positions$of$two $spherical$wave$fronts$are$shown$in$(a)$ with$theirdiverging$rays.$At$large$dista nces$from$the$source,$the$wave$fronts$be come$lessand$less$curved$and$approach$th e$limiting$case$of$a$plane&waveshown$in$ (b).$A$plane$wave$has$flat$wave$fronts$a nd$rays$parallel$toeach$ 1 of 1 Stickies3/30/14, 3:53 PMPage 1 of 1 Stickies3/30/14, 3:54 PMReflection*of*string*pulses*at*boundar ies*and*interfaces}}From&less&dense&medi umto&more&dense&mediumFrom&more&dense&me diumto&less&dense&mediumReflection&inver ted&&&&&&&&&Reflection&not&invertedPage 1 of 1 Stickies3/29/14, 11:56 PMLaw$of$reflection$of$waves$at$a$bounda ry$or$interface: i= r