The equation of the wave is $\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$ If the…
The equation of the wave is $\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$ If the displacement is $5 \mathrm{~cm}$ at $\mathrm{t}=0$ then the total phase at $\mathrm{t}=7.5 \mathrm{~s}$ will be $\left(\sin 30^{\circ}=0.5\right)$
$\frac{\pi}{3} \mathrm{rad}$
$\frac{\pi}{2} \mathrm{rad}$
$\frac{2 \pi}{5} \mathrm{rad}$
$\frac{2 \pi}{3} \mathrm{rad}$
Solution
$\begin{array}{ll} & \text { At } \mathrm{t}=0,10 \sin \left(\frac{2 \pi \times 0}{30}+\alpha\right)=5 \\ \therefore \quad & 10 \sin \alpha=5 \\ \therefore \quad & \sin \alpha=0.5 \\ \therefore \quad & \alpha=\frac{\pi}{6}\end{array}$
Thus, at $\mathrm{t}=7.5 \mathrm{~s}$,
$10 \sin \left(\frac{2 \pi \times 7.5}{30}+\alpha\right)=10 \sin \left(\frac{\pi}{2}+\frac{\pi}{6}\right)$
$\therefore \quad$ The total phase is $\frac{2 \pi}{3}$.