The bending of a wave around an obstacle or the edges of an opening is called diffraction.
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1 17.3 Diractin The bending a wae arund an btacle r the edge an pening i called diractin. 1
2 17.3 Diractin 2 dimenin: ingle lit irt minimum inθ λ D Linear Meaurement: D 1.4 cm, λ 0.6 cm redictin: inθ 0.6/ θ in -1 (0.43) 25 2
3 17.3 Diractin 2 dimenin: ingle lit irt minimum inθ λ D Linear meaurement: D 1.4 cm, λ 0.6 cm redictin: inθ 0.6/ θ in -1 (0.43) 25 3
4 17.3 Diractin 2 dimenin: ingle lit irt minimum inθ λ D Linear meaurement: D 1.5 cm, λ 0.6 cm redictin: inθ 0.6/ θ in -1 (0.43) 25 Angular meaurement: ~27 4
5 17.3 Diractin in 3 dimenin In 3D: Circular pening irt minimum: Similar but dierent reult than 2D Diameter circular pening (aperture) in θ Example: A lud peaker with diameter D30 cm, alternately generating und at 1500 and 8500 Hz. What are the cut- angle (1 t minima) r the tw requencie? λ D 5
6 17.3 Diractin in 3 dimenin In 3D: Circular pening irt minimum: Similar but dierent reult than 2D in θ λ D Diameter circular pening (aperture) Example: A lud peaker with diameter D30 cm, alternately generating und at 1500 and 8500 Hz. What are the cut- angle (1 t minima) r the tw requencie? Hz, Hz, and 343 m/ λ : λ / 343 m/ λ1 / m m/ λ2 / m inθ 1.22λ / D θ in (1.22λ / D) θ in 1 θ in (1.22)(0.229 m) m (1.22)( m) m 6
7 Exam 3 Reiew 21.6 Trque n Current Carrying Cil A cil wire N turn, area A, carrying current I ha magnetic mment: m NIA Strictly peaking, magnetic mment i a ectr in the directin the nrmal t the lp gien by RHR-2 relatie t the directin the current In unirm B ield, The cil experience a trque magnitude: τ (NIA) B inφ mbinφ φ i the angle between the nrmal the lp (the magnetic mment m ) and the magnetic ield B. The trque tend t align m with B τ Bar magnet ALSO hae magnetic mment Example: A mall mar magnet, (450g, r abut 1lb bar magnet ~25cm, r ~10 lng) ha a magnetic mment ~10Am 2 Cmparin (hmewrk): hydrgen atm: magnetic mment (rm rbiting electrn) ~10-23 Am 2 7
8 z 22.1 Induced current and ltage 22.2 Mtinal EMF Change in the magnetic ield thrugh a circuit lp caue an prduce an induced em and, in turn, induced current t lw. The change can be either in the magnitude r the directin the ield The change can be caued by a ming circuit, r by a ming urce the magnetic ield (e.g. a ming bar magnet) The ame happen i ne change the ize the circuit lp A traight egment a cnducting wire/rd/bar ming at peed perpendicular t it length L in a unirm magnetic ield B prduce a mtinal em E: y I x nrmal L Special cae we ued t tart Ch. 22: φ θ B I E ( B inθ ) BL cφ ( θ + φ L + B θ 90 E L BL inθ BL E 90 ) Thi rmula applie nly i, B, L are mutually perpendicular
9 22.3 Magnetic Flux Φ B Nrmal ectr Φ B BAcφ Directinal bundary path. Circulatin ene related t the nrmal ectr by RHR Faraday Law Inductin z y L x nrmal t t 0 φ θ B L Nrmal ectr One can think magnetic lux t be prprtinal t the number magnetic ield line thrugh a urace t t 0 nrmal + t φ θ B w Induced em : E BL cφ CW current Φ B( ) cφ w t Φ BL( w + t) cφ E 0 Lw E Φ t BL inθ Φ Φ t Same a mtinal em 0 BL( w + t) c φ BLwcφ BL( t) t t Any change in the lux (e.g. directin r trength the ield) Change in ize, hape, r rientatin lp) induce an em cφ
10 22.5 Lenz Law 1. Which way i the B ield thrugh the lp? up. 2. I the lux increaing r decreaing in the dir. B? increaing. 3. Increaing lux induced B ield pint in the ppite dir: dwn. 4. Induced current needed t generate DOWN ield: clck-wie (tp iew) The Magnetic ield i rtating in the directin hwn 1. Which way i the B ield thrugh the lp? up. 2. I the lux increaing r decreaing in the dir. B? decreaing. 3. decreaing lux induced B ield pint in the ppite dir: up. 4. Induced current needed t generate U ield: cunter-clck-wie (tp iew) Lenz Law analyi that ame circuit t determine the directin induced current z y L Induced current x nrmal Induced magnetic ield Lenz Law analyi: A ariatin n the ame theme z y L Induced current x nrmal Induced magnetic ield φ φ θ 10 B B
11 22.6 Generatr ω E BAω inθ E(t) LOO θ ωt r V (t) V (i equialent t) 22.9 Tranrmer E S Φ NS t + + Tranrmer equatin I S R V S E ( t ) E0 inωt r V ( t ) V inω 0 t eak em / urce ltage E E S E 0 N N S 0 V r rimary Cil: N lp NBAω V S V N N S Nte: E RMS Secndary Cil: N S lp E 0 2 E Φ N t Tranrmer cannt generate pwer I V I S V S I I p V V p N 11 N p
12 16.1 Wae Tranere Wae: particle mtin t wae directin Lngitudinal Wae: particle mtin t wae directin Nte that particle are NOT tranprted by the wae, nly energy (and inrmatin) 16.2 eridic Wae y x y t icture wae an intant in time Mtin particle at a ixed lcatin The medium take n a hape a ine cure, and thi hape trael. article in the medium d NOT trael: they execute imple harmnic Mtin in lace Aamplitude (max diplacement rm equilibrium), Tperid (time r ne cycle) λwaelengthditance between max-max r min-min 1/Trequency (Hz) wae peed: Unieral Wae Equatin: λ/t r λ 16.3 Speed Wae n a tring F m L Tenin (rce) in the tring linear denity ma per unit length 16.4 Math Decriptin y(x,t)a in(2πt ± 2πx/ λ) Set Calculatr t Radian Mde + r a wae traeling in the x directin r a wae traeling in the +x directin 12
13 16.5 Sund Wae Sund wae are lngitudinal cmprein wae Maximum reure/denity: Cndenatin Minimum reure/denity: Rareactin itch: related t requency: Eery ctae repreent an increae in requency actr 2 (lgarithmic repne) Ludne: related t preure amplitude Bilgical Repne t ludne i lgarithmic al 16.6 Speed Sund in a ga wae peed in m/ T ablute temperature in kelin m ma ga mlecule in kg (ue weighted aerage r mixture) γ kt m Speed Sund in Air at abut 20 C: 343 m/ 16.7 Sund Intenity I A wer Sund Surce Unit Intenity: W/m 2 2 Area 5 γ (mn - atmic gae like He, Ar) 3 7 r (diatmicgae likeo2, N2, H2) 5 23 k J K R / I 4π r 16.8 Intenity Leel: decibel β ( 10 db) lg( I / I ) I (ue weighted aerage r mixture) N A Fr an Itrpic urce: pwer i ditributed er the area a phere at ditance r W m 2 Lgarithmic bilgical repne Threhld human hearing 13
14 16.9 The Dppler Eect urce ming tward a tatinary berer urce ming away rm a tatinary berer Oberer ming tward tatinary urce Oberer ming away rm tatinary urce GENERAL CASE 1 ± 1 Numeratr: plu ign applie when berer me tward the urce Denminatr: minu ign applie when urce me tward the berer S O peed the und in medium peed urce rel. t medium peed berer rel. t medium 14
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