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(C) The equation of the wave is $y = 2 \sin(2\pi x - 100\pi t + \pi/3)$.For the particle to be at the mean position,the displacement $y$ must be $0$.S

Vedclass · Accepted Answer

$\frac{1}{300} 	ext{ s}$

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(C) The equation of the wave is $y = 2 \sin(2\pi x - 100\pi t + \pi/3)$.For the particle to be at the mean position,the displacement $y$ must be $0$.So,$2 \sin(2\pi x - 100\pi t + \pi/3) = 0$.This implies the argument of the sine function must be an integer multiple of $\pi$,i.e.,$2\pi x - 100\pi t + \pi/3 = n\pi$,where $n$ is an integer.Given $x = 4 	ext{ m}$,we substitute this into the equation:$2\pi(4) - 100\pi t + \pi/3 = n\pi$$8\pi - 100\pi t + \pi/3 = n\pi$$100\pi t = 8\pi + \pi/3 - n\pi = \frac{25\pi}{3} - n\pi$.To find the first time $t > 0$,we choose $n$ such that $t$ is positive and minimal. For $n = 8$:$100\pi t = \frac{25\pi}{3} - 8\pi = \frac{\pi}{3}$.$t = \frac{\pi/3}{100\pi} = \frac{1}{300} 	ext{ s}$.

$A$ sinusoidal progressive wave is generated in a string. Its equation is given by $y = (2 \text{ mm}) \sin(2\pi x - 100\pi t + \pi/3)$. The time when the particle at $x = 4 \text{ m}$ first passes through the mean position will be:

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