Question

The equation of a wave is given by y = 10 sin $\big(\frac{2 \pi}{45}t + \alpha\big)$.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)

$ y = 10 \sin \bigg[\frac{2 \pi}{45}t + \alpha\bigg]$
$ y = 5 \, cm \, at \, t = 0$
$\therefore 5 = 10 (\sin \, \alpha)$
or $ \sin \, \alpha = \frac{1}{2}$
or $ \alpha = \frac{\pi}{6}$
Again if $ t = 7.5 \, s$
Then total phase = $\frac{2 \pi}{45} \times \frac{15}{2} + \frac{\pi}{6}$
$ = \frac{\pi}{3} + \frac{\pi}{6}$
$ = \frac{2 \pi + \pi}{6}$
$ = \frac{3 \pi}{6} = \frac{\pi}{2}$