Question

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

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

Answer 1

Answer: (B)

$\frac{\pi}{2}$

Answer 2

The given equations of a wave is

$y = 10\sin\left( \frac{2\pi}{45}t + \alpha \right)$

At t = 0, y = 5cm

$\therefore 5 = 10\sin\alpha$

$\frac{1}{2} = \sin\alpha$

$\sin\left( \frac{\pi}{6} \right) = \sin\alpha$

$\alpha = \frac{\pi}{6}$ ….. (i)

Hence, the total phase at

$t = 7.5s\left( = \frac{15}{2}s \right)$

$\varphi = \frac{2\pi}{45} \times \frac{15}{2} + \alpha = \frac{\pi}{3} + \frac{\pi}{6}$ (Using (i))

$= \frac{3\pi}{6} = \frac{\pi}{2}$