Question

The equation of a wave is given by
$y=10$ sin$(\frac{2\pi }{45}t+\alpha )$.
If the displacement is $5cm$ at $t=0$, the the total phase at $t=7.5s$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{6}$
• D. $\pi$

Answer 1

The correct option is B $\frac{\pi }{2}$

The given equation of wave is
$y=10$ sin $(\frac{2\pi }{45}t+\alpha )$
At $t=0,y=5cm$
$\therefore 5=10$ sin$\alpha$
$\frac{1}{2}=$ sin $\alpha$ or sin $\left(\frac{\pi }{6}\right)=$ sin$\alpha$
$\alpha =\frac{\pi }{6}$ ......(i)
hence, the total phase at $t$ = $7.5s=\left(\frac{15}{2}s\right)$ is
$\varphi =\frac{2\pi }{45}\times \frac{15}{2}+\alpha =\frac{\pi }{3}+\frac{\pi }{6}$ (Using (i))
$\alpha =\frac{3\pi }{6}=\frac{\pi }{2}$