- #1
rusty65
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Homework Statement
A transverse wave on a cord is given by D(x, t) = 0.19sin(2.9x - 35t), where D and x are in m and t is in s.
1) At t = 8.6*10^-2 s, what is the displacement of the point on the cord where x = 0.62 m?
2) At t = 8.6*10^-2 s, what is the velocity of the point on the cord where x = 0.62 m?
Homework Equations
given displacement ---> D(x, t) = 0.19sin(2.9x - 35t)
The Attempt at a Solution
I didnt have any trouble finding the displacement of the wave along the cord (-0.18m) as all I had to do was plug in the given values of x and t, then make sure my calculator was in radians.
The velocity is where I ran into problems. I figured it shouldn't be any harder than taking the derivative of the given equation, then once again plugging in the supplied values. However, I did not come up with the correct answer, and I not sure if I simply differentiated incorrectly or if that is not even the correct approach. Heres my work:
0.19sin(2.9x - 35t) ---> ∂D/∂t = 0.19cos(2.9x - 35t) * (2.9 - 35t)
∂D/∂t = 0.19cos(2.9x - 35t) * (2.9 - 3.01) = (-0.11)*0.19cos(2.9x - 35t)
∂D/∂t = -0.0209cos(2.9x - 35t)
∂D/∂t = -0.0209cos(-1.212)
∂D/∂t = -0.007338 m/s
But, like I said, ∂D/∂t =/= -0.007338 m/s
Any help would be greatly appreciated.