450fall09hw10_Sol - ECE 450 Fall 2009 Homework 10 Solutions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE 450 Fall 2009 Homework 10 Solutions Due: Tuesday, Nov 3 rd , 2009 1. The medium is dispersive, i.e., different frequency components will travel at different speeds, which is determined by the dispersion relation given as gk ω = . a. Given the relationships for v p and v g , express both them as a function of frequency ω what the dispersion relation indicates. There are a couple of ways to approach the problem, all of which lead to the same results. i. Given gk = , 2 2 p gk g k gg v kk ωω = =⇒= = = () 2 2 2 2 g gk gk gk g g v k =→ = ∂∂ =⇒ = == ii. Æ Given gk = and the fact that p k v = , 2 p p p g v g gv v = =♠ Æ Proceed with using k directly on the dispersion relation to determine v g . 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
() 1 1 g 2 2 · 2 2 Using , 2 g gk gk g kk gk k g g v k ω ∂∂ TT == = = ** Relationship: v g = 1/2 v p and as a side note, notice how both decreases as frequency increases. b. So the rock falling into the calm, deep ocean creates a spectrum waves with periods longer than T min and shorter than T max , i.e., im T in ax m , ( T i exemplifies the period of an individual frequency component). Given the fact that the period T is inverse proportional to frequency (i.e., 1 T ), you can equate x min ma T and n max mi T ax --
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

450fall09hw10_Sol - ECE 450 Fall 2009 Homework 10 Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

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