# Crib3Edited - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

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Constants k=1/(4 πε 0 )=8.99x10 9 (N*m 2) /C 2 ε 0 =8.85x10 -12 C 2 /(N*m 2 ) e - = -1.6 x 10 -19 C μ 0 =4πe-7 H/m μ 0 =1.26x10 -6 c=speed of light=3.0 x 10 8 m/sec speed of sound (air) = 343 m/sec Area Circle = π r 2 Circumference Circle = 2 π r Surface Area Sphere = 4 π r 2 Φ B = Magnetic Flux (Weber, W) Φ E = Electric Flux ((N*m 2) /C) B = Magnetic Field (Tesla, T) L = Inductance (Henry, H) Є = emf (volts) I = Intensity (W/m 2 ) E m : (V/m) c = E m /B m h = 6.63 x 10 -34 J*sec *** h = 4.14 x 10 -15 eV*sec 1 eV = 1.6 x 10 -19 J m electron = 9.11 x 10 -31 kg Energy and Waves I = P/A = P/ (4 π r 2 ) Point Source : I α 1/r 2 α E 2 EM Waves ( E m α 1/r ) S =(1/μ 0 ) E x B Poynting Vector I=(1/2μ 0 )E m B m I = E m 2 /(2μ 0 c) I = cB m 2 /(2μ 0 ) S S varies w/ time, work with avg. intensity RMS Values E rms = E m /√2 I=(1/μ 0 )E rms B rms = E rms 2 /(cμ 0 ) = cB rms 2 0 Radiation Pressure Pressure = F/A = p r A = area that intercepts waves p r = I/c complete absorption p r = 2I/c complete reflection Sound Waves I=(1/2)ρ v ω 2 s m 2 s m = displacement amp. I = Δp m 2 /(2ρ v ) Δp m = pressure amp. I α r 2 β=(10db)log(I/I 0 ) (I/I 0 )=10 (Δβ/10) Sound level I 0 = 10 -12 W/m 2 Wave Scattering When EM waves or sound waves interact with matter, the scattered and incident waves may have different ω, λ, etc… Special Cases: 1. Wave propagating thru a different material (refraction) 2. Scattering from an object or aperture (diffraction) 3. Reflection Refraction: Waves in different materials have diff. wave speeds For EM waves (light): v = c (vacuum) c > v = c/n (matter); n – index of refraction (n μ 1.0) When EM waves or sound waves enter a new material they: Reflect part of their energy Transmit part of their energy into the material Retain ω and ø (mostly) v changes, λ changes, f stays constant λ n = v n /f = (c/n)*(1/f) = λ/n Snell’s Law of Refraction: n 1 sinθ 1 =n 2 sinθ 2 Interference Waves from 2 sources add together at each point in space (superposition principle). Resulting intensity changes w/ position Wave traveling in distance L has phase angle kL Δø = kL 1 – kL 2 = ΔL*(2π/λ) *diff. lengths Constructive Interference: ΔL = mλ Destructive Interference: ΔL = (m+½)λ m = 0,1,2,3… Δø = kL 2 – kL 1 = L(2π/ λ 2 - 2π/ λ 1 ) *diff. materials

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## This note was uploaded on 04/07/2008 for the course ENG 1000 taught by Professor Broomer during the Spring '08 term at Rensselaer Polytechnic Institute.

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Crib3Edited - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

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