Question

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

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