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Figure shows a snapshot ofasinusoidaltravelling wave taken at t =0.35. The wavelength is 7.5 cm and the amplitude is 2cm. Ifthe crest P was at x = 0 at t = 0, write the equation ot travelling wave. |
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Answer» Solution :GIVEN, `A=2cm, lambda= 7.5 cm` `:. K =(2pi)/lambda = 0.84 cm^(-1)`  The WAVE has TRAVELLED a distance of 1.2 cm in 0.3s. Hence, SPEED ofthe wave, ` v =1.2/0.3 = 4 cm//s` `:.` Angular frequency `omega =(v)(k) = 3.36 red//s` Since the wave is travelling along positive x-direction andcrest (maximum displacement) is at x = 0 at t = 0, we can WRITE the wave equation as, `y = A sin (kx - omegat + pi/2) (or ) y (x,t) = A cos (kx- omegat)` `y (x,t) = (2 cm) cos [0.84cm^(-1)x -(3.36 rad//s)t] cm` |
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