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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
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.
$\frac{\lambda }{{2\pi }}\left( {\phi + \frac{\pi }{2}} \right)$
b
(b) ${y_1} = {a_1}\sin \,\left( {\omega \,t - \frac{{2\pi x}}{\lambda }} \right)$ 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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