Question

1) A square energy pulse traveling to the right with a speed v-2 m/s is given by the equation: f(x,t)-E if Ix-vtl<a f(x,t)-0 if lx-vtla where E is an energy constant and a a length constant. i) Plot this pulse as a funtion of x at t-0. ii) Plot this pulse as a function of x at t-4 s. iii) Expand this pulse as an infinite superposition of harmonic traveling waves of the type cos(ot-kx) where co/k-v.

Answer 1

Sdf Given sqvame wave. pulse hnarelling to right ui th speed 2 m/s , with eqohn, f(x, t) = E, if Ix-yat ka (i) at tso, {(x,o) = if E I1Ka от and a ) ii) At t=4s, we hare ) + a u sing this, we can plot ,4) ar chosn, 8-a (iii) using oun eỉotheotem) we can alwayswik i k(x-vt) when i C(k) = from, e9-0) we get) Given efa-yt) et+a inot atyt et-a zaCe

Ra ikq + - σ丫 !e(K) = E sin (ka) | | We have uoed sin (ka) = ee 2i 几K į ( kx-wt) dk