Question

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

Moderate

Solution

We now that $v_{\max} = aω and v = nλ$
$∴ \frac{v_{\max}}{v} = \frac{aω}{nλ} = \frac{a (2 πn)}{nπ} = \frac{2 πa}{λ}$
= $\frac{2 πa}{\frac{2 π}{k}} = ka = \frac{π}{2} \times 3 = \frac{3 π}{2}$

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