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Question

The equation for a wave travelling in x-direction on a string : y=(3.0cm)sin[(3.14x)(314t)]
Find the maximum velocity of a particle of the string
Find the acceleration of a particle at x = 60 cm at time = 0.11 s

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Solution

Equation of ave is y=3.0sin[(3.14x)3.14t)]
here k=3.14,ω=314
so wave velocity =ωk=3143.14=100cm/s
acceleration of particle is given by
ap=2yt2=3.0×3142sin[(3.14x)(314t)]
Acceleration of particle at x=60cm,k=0.11s
ap=3.0×(314)2sin[(3,14×60)(314×0.11)]230.6m/s

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