Question

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

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

Answer 1

Answer: (A)

$(\frac{2\pi }{3})rad$

$y=10\sin (\frac{2\pi t}{30}+\alpha )$
$y=A\sin (\omega t+kx)$
$\therefore att=0,y=5$
$5=10\sin (0+\alpha )$
$\alpha =\frac{\pi }{6}$
$y=10\sin (\frac{2\pi \times t}{30}+\frac{\pi }{6})$
$=10\sin (\frac{\pi }{2}+\frac{\pi }{6})$ at $t=7.5sec$
$=10\sin \left(\frac{2\pi }{3}\right)$
$\therefore \varphi =\frac{2\pi }{3}$