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Question

The equation for a wave travelling in x direction on a string is given as
y=10sin(πt0.5x), where y and x are in m and time(t) in sec. Find the acceleration of a particle at x=π m at time t=1 sec.

A
10π m/s2
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B
10π2 m/s2
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C
5π m/s2
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D
5π m/s2
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Solution

The correct option is B 10π2 m/s2
We know,
Velocity of particle vP=yt=10πcos(πt0.5x)
Similarly, acceleration of particle can be obtained by partial differentiation of velocity w.r.t time (keeping x constant).
aP=vPt
aP=π×10πsin(πt0.5x)
aP=10π2sin(πt0.5x)
substituting x=π m & t=1 sec in above equation we get,
aP=10π2sin(π0.5π)
aP=10π2sinπ2
aP=10π2 m/s2

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