PHYS 422 Lecture 11 Superposition III

PHYS 422 Lecture 11 Superposition III - The Superposition...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The Superposition of Waves III Anharmonic Periodic Waves Superposition of harmonic waves leads periodic but anharmonic wave to periodic but anharmonic wave Fourier Series Fourier’s Theorem: any function f ( x ) that has a spatial period λ can be synthesized by a sum of harmonic functions whose avelengths are integral submultiples of wavelengths are integral submultiples of λ ( λ , λ /2, λ /3, … ) . 2 s 2 s ⎞ ⎛ ⎞ ⎛ = π π x x ( ) ... 2 / cos cos 2 2 1 1 + ⎟ ⎠ ⎜ ⎝ + + ⎟ ⎠ ⎜ ⎝ + + ξ λ ξ λ C C C x f represents component with λ = ∞ , i.e. series for λ /0 , λ /1, λ /2, … traveling wave: f ( x- v t ) k =2 π / λ ( ) ( ) ( ) ( ) ... cos ... 2 cos cos 2 2 1 1 + + + + + + + + = m m mkx C kx C kx C C x f ξ ξ ξ kx kx kx n s s ( ) ( ) ( ) mkx B mkx A mkx C m m m m sin cos cos + = +ξ Fourier Series ( ) ( ) ( ) ∑ ∑ ∞ = ∞ = + + = 1 1 sin cos 2 m m m m mkx B mkx A A x f Can be shown (page 304): ( ) ( ) ∫ = λ λ cos 2 dx mkx x f A m ( ) ( ) ∫ = λ λ sin 2 dx mkx x...
View Full Document

This note was uploaded on 03/23/2011 for the course PHYS 422 taught by Professor Staff during the Spring '08 term at Purdue.

Page1 / 13

PHYS 422 Lecture 11 Superposition III - The Superposition...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online