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Q.
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 $t = 0$, then the total phase at $t = 7.5\, sec$ will be
Given: Equation of wave
$y=10 \sin \left(\frac{2 \pi t}{30}+\alpha\right) ;$ Displacement $(y)=5\, cm ;$ Initial
time $\left(t_{1}\right)=0$ and final time $\left(t_{2}\right)=7.5 \,sec$.
We know that displacement of the wave at $t=0$
$y=a \sin \alpha=10 \sin \alpha$ or $\sin \alpha=\frac{1}{2}$ or $\alpha=\frac{\pi}{6} .$ Therefore
total phase at $t=7.5, \phi=\frac{2 \pi \times 7 \cdot 5}{30}+\frac{\pi}{6}=\frac{\pi}{2}+\frac{\pi}{6}=\frac{2 \pi}{3}$.