The minimum phase difference between two simple harmonic motions is
$x_1 = \dfrac{1}{\sqrt{2}} \sin \omega t + \dfrac{1}{\sqrt{2}} \cos \omega t$
$x_2 = \sin \omega t + \cos \omega t$     $\left[ \sin \dfrac{\pi}{4} = \cos \dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}} \right]$

A pendulum clock is running slow, In order to correct it, we should

A simple harmonic progressive wave is represented by $y = A \sin(120\pi t + 3x)$. The distance between two points on the wave at a phase difference of $\dfrac{\pi}{3}$ radian is

A pipe open at both ends has a fundamental frequency 'f' in air. The pipe is dipped in water, so that $\dfrac{2}{3}^{rd}$ length of pipe is in water, Now the fundamental frequency of the air column is