Question

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

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