Two waves are represented by the equations : $y_1 = a\, sin\,(\omega t + kx + 0.57)\, m$ and $y_2 = a\, cos\,(\omega t + kx)\, m$, where $x$ is in $metres$ and $t$ is in $seconds$ . The phase difference between them is ..... $radian$
AIPMT 2011, Medium
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${{\rm{y}}_1} = {\rm{a}}\sin (\omega {\rm{t}} + {\rm{kx}} + 0.57)$
$\therefore$ Phase, $\phi_{1}=(\omega t+k x+0.57)$
$y_{2}=\operatorname{acos}(\omega t+k x)=a \sin \left(\omega t+k x+\frac{\pi}{2}\right)$
$\therefore$ Phase, $\phi_{2}=\omega t+k x+\frac{\pi}{2}$
Phase difference, $\Delta \phi=\phi_{2}-\phi_{1}$
$=\left(\omega t+k x+\frac{\pi}{2}\right)-(\omega t+k x+0.57)$
$=\frac{\pi}{2}-0.57=1.57-0.57=1 \mathrm{\,radian}$
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