The-incident-wave-set-up-on-a-string-of-length-fixed-at-each-end-is-given-by-y-1-Asin-kx-wt-i-what-is-the-equation-of-motion-of-the-reflected-wave-y-2-ii-obtain-the-resultant-y-y-1-y-2-of-the

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Question Number 38822 by NECx last updated on 30/Jun/18

$$Theincidentwavesetuponastring$$$$oflengthfixedateachendisgiven$$$$by:y_1=Asin(kx-wt)$$$$i)whatistheequationofmotion$$$$ofthereflectedwave,y_2.$$$$ii)obtaintheresultant,y=y_1+y_2$$$$ofthetwowaves.$$$$iii)whattypeofresultantwaveis$$$$this?$$$$iv)forwhatvaluesofxwillthe$$$$amplitudoftheresultantwave$$$$becomezero?$$$$v)forwhatvaluesofxwillybe$$$$maximum?$$

Commented by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jun/18

$$i)y_2=Asin(kx+wt)$$$$ii)y_1+y_2=Asin(kx-wt)+Asin(kx+wt)$$$$=2Asin\left(kx\right)coswt$$$$iii)standingwave$$$$iv)amplitude=2Asinkx$$$$maxamplitude=2Aminamplitude=0$$$$whensinkx=0=sinn\mathrm{\Pi }$$$$kx=n\mathrm{\Pi }x=\frac{n\mathrm{\Pi }}{k}=\frac{n\mathrm{\Pi }}{2\mathrm{\Pi }}\times \lambda =n\frac{\lambda }{2}$$$$v)maxamplitude=2Awhensinkx=\pm 1$$$$$$$$sinkx=sin(n+\frac{1}{2})\mathrm{\Pi }$$$$kx=(n+\frac{1}{2})\mathrm{\Pi }$$$$\kappa =\frac{2\mathrm{\Pi }}{\lambda }$$$$2\frac{\mathrm{\Pi }}{\lambda }x=(n+\frac{1}{2})\mathrm{\Pi }$$$$x=(n+\frac{1}{2})\frac{\lambda }{2}$$$$$$$$$$

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