Question

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

• A. $\frac{2\pi }{3}rad$
• B. $\frac{\pi }{3}rad$
• C. $\frac{\pi }{2}rad$
• D. $\frac{2\pi }{5}rad$

Answer 1

Answer: (A)

Given: Equation of wave
$y=10\sin \left(\frac{2\pi t}{30}+\alpha \right);$ Displacement $(y)=5cm;$ Initial
time $\left(t_1\right)=0$ and final time $\left(t_2\right)=7.5sec$.
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 $t=7.5,\varphi =\frac{2\pi \times 7\cdot 5}{30}+\frac{\pi }{6}=\frac{\pi }{2}+\frac{\pi }{6}=\frac{2\pi }{3}$.