Two SHM are given by $y_1=\text{A}\sin \left(\frac{\pi }{2}\text{t}+\varphi \right)\text{ and }{y}_2=\text{B}\sin \left(\frac{2\pi }{3}+\varphi \right)$ . The phase difference between these two after ‘1’ sec is

$y_1=\text{A}\sin \left(\frac{\pi }{2}\text{t}+\varphi \right)$

$y_2=\text{B}\sin \left(\frac{2\pi }{3}+\varphi \right)$

After t = 1 sec; $\Delta \varphi =?$

${\varphi }_1=\frac{\pi }{2}\text{t}+\varphi$

${\varphi }_2=\frac{2\pi }{3}+\varphi$

$\Delta \varphi ={\varphi }_2-{\varphi }_1$

$=\frac{2\pi }{3}\text{t}-\frac{\pi }{2}\text{t}$

$\Delta \varphi =\frac{2\pi }{3}-\frac{\pi }{2}\left(\because \text{t}=1\sec \right)$

$\Delta \varphi =\frac{\pi }{6}$