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
B
3π
C
23π
D
2π

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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