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A transvers sinusoidal wave move along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm . At a particular time t, the snap-shot of the wave is shown in figure . The velocity of point P when its displacement is 5 cm is : |
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Answer» <P>`(sqrt(3 pi))/(50 ) hatj` m/s Here `(dy)/(dx) ` is negative . Therefore,velocity at point P ispositive and is along y-axis only. ALITER Equations of a wave moving in positive x-a-axisis given as y = A sin `(OMEGA t - phi ) or V_(p) = A omega cos (omega t - phi) ` Here y= 5 cm , A = 10 cm, `therefore 5= 10 sin (omega t - phi) rArr omega t - phi = 30^(@)` Subsitituting this value in the quation of velocity we get `V_(p) = 0.10 xx omega cos 30^(@)` Now V = v `LAMBDA "" therefore v= (v)/(lambda) = (0.10)/(0.5)= 0.2` `therefore omega = 2pi v= 2pi xx 0.2 = 0.4 pi` `rArr v_(P) = 0.1 xx 0.4 pi xx (sqrt(3))/(2) = (sqrt(3))/(50 ) pi ` It has to be in positive y direction. So correct choice is (a). |
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