MCQ
The path difference between the two waves $y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and $y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)$ is
  • A
    $\frac{\lambda}{2 \pi} \phi$
  • $\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
  • C
    $\frac{2 \pi}{\lambda}\left(\phi-\frac{\pi}{2}\right)$
  • D
    $\frac{2 \pi}{\lambda} \phi$

Answer

Correct option: B.
$\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$
$y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right)$ and$y_2=a_2\cos\left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)=a_2 \sin \left(\omega t-\frac{2 \pi x}{\lambda}+\phi+\frac{\pi}{2}\right)$
So phase difference $=\phi+\frac{\pi}{2}$ and $\Delta=\frac{\lambda}{2 \pi}\left(\phi+\frac{\pi}{2}\right)$

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