1 2 taylorseriesexpand f f 0 1 f

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Unformatted text preview: oth cases ! f’/f ONLY DEPENDS ON THE RELATIVE VELOCITY 1 2 1+ β f′= f ÷ 1− β Doppler Shift for E&M Waves Doppler Shift for E&M Waves A Note on Approximations 1 2 1+ β f′= f ÷ 1− β f ′ ≈ f ( 1+ β ) β << 1 WHY ?? 1/ 2 Taylor Series: Expand F ( β ) = F ( 0) + 1+ β F (β ) = 1− β F ′(0) F ′′(0) 2 β+ β + ... 1! 2! Evaluate: F (0) = 1 F ′(0) = 1 around β = 0 F (β ) ≈ 1 + β Doppler Shift for E&M Waves Doppler Shift for E&M Waves A Note on Approximations 1 2 1+ β f′= f ÷ 1− β f ′ ≈ f ( 1+ β ) β << 1 1/ 2 Taylor Series: Expand 1+ β F (β ) = 1− β around β = 0 F ′(0) F ( β ) ≈ F (0) + β = 1+ β 1! F ′(0) = NOTE: F ( β ) = (1 + β )1 / 2 F (β ) ≈ 1 + 1 β 2 Red Shift Wav...
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This document was uploaded on 02/13/2014.

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