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Question

The equation of a simple harmonic wave is given by
$$y=3\sin{\cfrac{\pi}{2}(50t-x)}$$
where $$x$$ and $$y$$ are in meters and $$t$$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:


A
32π
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B
3π
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C
23π
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D
2π
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Solution

The correct option is D $$\cfrac{3}{2}\pi$$
From the wave equations, we know that
$${v}_{max}=a\omega$$
$$v=n\lambda$$
$$\cfrac{{v}_{max}}{v}=\cfrac{a\omega}{n\lambda}=\cfrac{a(2\pi n)}{n\lambda}=\cfrac{2\pi a}{\lambda}=\cfrac{2\pi a}{\cfrac{2\pi}{K}}$$
$$=Ka=\cfrac{\pi}{2}\times 3=\cfrac{3\pi}{2}$$

Physics

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