L04_a - Sinusoidal Traveling Waves(13.3 in text • For any...

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Unformatted text preview: Sinusoidal Traveling Waves (13.3 in text) • For any traveling wave, expect ( ) ( ) vt x f t x y − = , o Ask: what is the form of function f for a sinusoidal wave with: ¡ specific speed v ¡ specific wavelength λ First: look at x dependence of sinusoidal wave function: • To start, choose = t to be time when y vs x (i.e. “snap-shot” of string) looks like kx A y sin = . o (Will see what k is soon.) • Argument of kx A y sin = (i.e. kx ) increases by π 2 when x increases by λ o So wave function at = t must have form ( ) = x A x y λ π 2 sin , o Says λ π 2 = k (will call this angular wave number) Second: look at t dependence of sinusoidal wave function: • At time t , wave has moved distance xt to the right: o So: ( ) ( ) , , vt x y t x y − = o In words: At time t , value of y for a given x is the same as what y was at t =0 and a distance vt to the left. • Combine with result for x dependence to get: o ( ) ( ) − = vt x A t x y λ π 2 sin , o has required form ( ) ( ) vt x f t x y − = , for traveling wave Alternate ways to write wave function for traveling sinusoidal wave: • For one alternate version: o use T v λ = so that T v 1 = λ ....
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This note was uploaded on 03/08/2012 for the course PHYSICS 1051 taught by Professor Michaelmorrow during the Winter '12 term at Memorial University.

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L04_a - Sinusoidal Traveling Waves(13.3 in text • For any...

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