The equation of a wave is given by y = 10 sin | vedclass

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

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

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(D) The given wave equation is $y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$.At $t = 0 \ s$,the displacement $y = 5 \ cm$.Substituting these values into the equation: $5 = 10 \sin \left(\frac{2 \pi (0)}{30} + \alpha\right) \implies 5 = 10 \sin \alpha \implies \sin \alpha = \frac{1}{2}$.Thus,the initial phase constant $\alpha = \frac{\pi}{6} \ rad$.The total phase angle $\phi$ at any time $t$ is given by $\phi = \frac{2 \pi t}{30} + \alpha$.At $t = 7.5 \ s$,the total phase angle is $\phi = \frac{2 \pi (7.5)}{30} + \frac{\pi}{6}$.$\phi = \frac{15 \pi}{30} + \frac{\pi}{6} = \frac{\pi}{2} + \frac{\pi}{6}$.$\phi = \frac{3 \pi + \pi}{6} = \frac{4 \pi}{6} = \frac{2 \pi}{3} \ rad$.

The equation of a wave is given by $y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$. If the displacement is $5 \ cm$ at $t = 0 \ s$,then the total phase angle at $t = 7.5 \ s$ will be:

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