Physics - Wave on String Question with Solution | TestHub

Given waves are $Y_1=a_1\sin \left(\omega t-\frac{2\pi x}{\lambda }\right)$ and $Y_2=a_2\cos \left(\omega t-\frac{2\pi x}{\lambda }+\Phi \right)$.

Expressing $Y_2$ in terms of sine function:

$Y_2=a_2\sin \left(\omega t-\frac{2\pi x}{\lambda }+\Phi +\frac{\pi }{2}\right)$

The phase difference $\Delta \varphi$ between the two waves is:

$\Delta \varphi =\left(\omega t-\frac{2\pi x}{\lambda }+\Phi +\frac{\pi }{2}\right)-\left(\omega t-\frac{2\pi x}{\lambda }\right)=\Phi +\frac{\pi }{2}$

The relation between path difference $\Delta x$ and phase difference $\Delta \varphi$ is given by:

$\Delta x=\frac{\lambda }{2\pi }\Delta \varphi$

Substituting the value of $\Delta \varphi$:

$\Delta x=\frac{\lambda }{2\pi }\left(\Phi +\frac{\pi }{2}\right)$

Answer: $\frac{\lambda }{2\pi }\left(\Phi +\frac{\pi }{2}\right)$