The equation of a wave is y(x,t)=0.1sin[π3(10x−30t)−π6]m.
Find the acceleration of the particle at x=0.85m and t=0.25s
[Assume, π2=10 ; ↑ denotes positive y−direction and ↓ denotes negative y−direction ]
A
40m/s2↑
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B
50m/s2↓
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C
40m/s2↓
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D
50m/s2↑
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Solution
The correct option is B50m/s2↓ Given ,
Equation of the wave is y(x,t)=0.1sin[π3(10x−30t)−π6]m
Differentiating twice on both sides with respect to time,
dydt=0.1cos[π3(10x−30t)−π6]×(−10π)
d2ydt2=(−π)sin[π3(10x−30t)−π6]×(+10π)
So, acceleration of particle d2ydt2=−10π2sin[π3(10x−30t)−π6]
at x=0.85m&t=0.25sec we get ,
a=−10π2sin[π3(8.5−7.5)−π6]
⇒a=−10π2sin(π6)=−50m/s2
Thus, option (b) is the correct answer.