A progressive wave having amplitude $5 m$ and wavelength $3 m$ . If the maximum average velocity of particle half time period is $5 m / s$ and wave is moving in the positive x-direction then find which may be the correct equation(s) of the wave? [where $x$ in meter]

5 sin (\frac{2 π}{5} t - \frac{2 π}{3} x)

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4 sin (\frac{2 π}{2} t - \frac{2 π}{3} x) + 3 c o s (\frac{2 π}{2} - \frac{2 π}{3} x)

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5 sin (\frac{π t}{2} - \frac{2 π}{3} x)

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3 cos (\frac{2 π}{5} t - \frac{2 π}{3} x) - 4 sin (\frac{2 π}{5} - \frac{2 π}{3} x)

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Solution

The correct option is C $5 sin (\frac{π t}{2} - \frac{2 π}{3} x)$
$\begin{matrix} V_{a v} = \frac{2 A}{(T / 2)} 5 m / s = \frac{4 A}{T} \Rightarrow 5 = \frac{4 \times 5}{T} \Rightarrow T = 4 sec = \frac{2 π}{w} w = \frac{π}{2} ∴ y = 5 sin (\frac{π t}{2} - \frac{2 π}{3} x) H e n c e, o p t i o n C i s c o r r e c t a n s w e r . \end{matrix}$

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