Question

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