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For the transverse wave equation y=A \sin (\pi x+\pi t), choose the correct options at t=0

Option: 1

Points at x=0 and x=1 are at mean position


Option: 2

Points at x=0.5 and x=1.5 have maximum acceleration


Option: 3

Points at x=0.5 and x=1.5 are at rest


Option: 4

The given wave is traveling in positive x-direction


Answers (1)

best_answer

y=A \sin (\pi x+\pi t)

V_p=\frac{\partial y}{\partial t}=\pi A \cos (\pi r+\pi t)

\text { At } t=0, x=0.5,1.5

\Rightarrow v=0, \quad a_p=\frac{\partial^2 y}{\partial t^2}=-\pi^2 A \sin (\pi x+\pi t)

\text { At } t=0, x=0.5,1.5 acceleration is max. And since, \omegat and kx are of same sign, hence the wave is travelling in negative x-direction

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