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A simple harmonic plane wave propagatees along x-axis in a medium. The displacement of the particle as a function of time is shown in figure, for `x=0`(curve 1) and `x=7` (curve 2) The two particle are with a span of onewavelength. The speed of the wave isA. `12 m//s`B. `24 m//s`C. `8 m//s`D. `16 m//s` |
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Answer» Correct Answer - a Let general wave equation be `y=A sin(omegat-kx+phi)` `v=(dy)/(dt)= Aomega cos(omegat-kx+phi)` For curve `(1),x=0` at `t=0,x=0,` we have `y=0` `implies 0=A sin [phi]implies sin phi=0` `implies phi=0` or `pi` here `phi=pi` (because velocity is negative) for curve `(2),xx=7 cm` `t=0,x=7 cm, y=-1` `-1=sin(-kxx7+pi)` `implies sin(-7k+pi)=-1//2` `implies-7k+pi=2npi+(7pi)/(6)` or `2npi+(11pi)/(6)` here `implies-7k+pi=2npi+(11pi)/(6)` (because at `t=0`, velocity is positive) `implies-7((2pi)/(lambda))=2npi+(5pi)/(6)` implieslammbda=(-14pi)/((5pi)/(6)+2npi)` ` `implieslambda=(-84)/(12n+5)` for `n=-1,lambda=12 cm` for `n=-2,lambda=(84)/(19)cm` (not possible) because `lambdagt7 cm` `v=flambda=100xx(12)/(100)=12 m//s` |
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