The equation of wave is given by $y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right)$. If the displacement is…
The equation of wave is given by $y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right)$. If the displacement is $5 \mathrm{~cm}$ at $\mathrm{t}=0$, then the total phase angle at $\mathrm{t}=7.5 \mathrm{~s}$ will be
$\frac{\pi}{3} \mathrm{rad}$
$\frac{\pi}{2} \mathrm{rad}$
$\frac{2 \pi}{5} \mathrm{rad}$
$\frac{2 \pi}{3} \mathrm{rad}$
Solution
$\mathrm{y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)$
At $\mathrm{t}=0, \mathrm{y}=5 \mathrm{~cm}$
$5=10 \sin \alpha$
$\alpha=\frac{\pi}{6}$
At $\mathrm{t}=7.5$, the total phase
$\phi=\frac{2 \pi \times 7.5}{30}+\alpha=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3} \mathrm{rad}$