Question

If $x=a\sin (\omega t+\pi /6)$ and $x^{\prime }=a\cos \omega t$, what is the phase difference between the two waves?

• A. $\frac{\pi }{3}$
  
• B. $\frac{\pi }{6}$
  
• C. $\frac{\pi }{2}$
  
• D. $\pi$

Answer 1

The correct option is A $\frac{\pi }{3}$


Given:
$x=a\sin (\omega t+\frac{\pi }{6})$
$x^{\prime }=a\cos \omega t=a\sin (\omega t+\frac{\pi }{2})$
Therefore, the phase difference between the two waves is given by,
$\Delta \varphi =\frac{\pi }{2}-\frac{\pi }{6}=\frac{\pi }{3}$

Hence, $\left(A\right)$ is the correct answer.