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(D) The given wave equation is $Y = 10 \sin \left(\frac{2 \pi t}{30} + \alphaight)$.At $t = 0$,the displacement $Y = 5 	ext{ cm}$.Substituting thes

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$\frac{2 \pi}{3} 	ext{ rad}$

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(D) The given wave equation is $Y = 10 \sin \left(\frac{2 \pi t}{30} + \alphaight)$.At $t = 0$,the displacement $Y = 5 	ext{ cm}$.Substituting these values: $5 = 10 \sin \left(\frac{2 \pi 	imes 0}{30} + \alphaight)$.$5 = 10 \sin \alpha \implies \sin \alpha = 0.5$.Since $\sin 30^{\circ} = 0.5$,we have $\alpha = 30^{\circ} = \frac{\pi}{6} 	ext{ rad}$.The total phase $\phi$ at any time $t$ is given by $\phi = \frac{2 \pi t}{30} + \alpha$.At $t = 7.5 	ext{ s}$:$\phi = \frac{2 \pi 	imes 7.5}{30} + \frac{\pi}{6}$.$\phi = \frac{15 \pi}{30} + \frac{\pi}{6} = \frac{\pi}{2} + \frac{\pi}{6}$.$\phi = \frac{3 \pi + \pi}{6} = \frac{4 \pi}{6} = \frac{2 \pi}{3} 	ext{ rad}$.

The equation of the wave is $Y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$. If the displacement is $5 \text{ cm}$ at $t = 0$,then the total phase at $t = 7.5 \text{ s}$ will be (Given: $\sin 30^{\circ} = 0.5$)

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