On the superposition of two harmonic oscillations represented by ${x_1} = a\,\sin \,\left( {\omega t + {\phi _1}} \right)$ and ${x_2} = a\,\sin \,\left( {\omega t + {\phi _2}} \right)$ a resulting oscillation with the same time period and amplitude is obtained. The value of ${\phi _1} - {\phi _2}$ is .... $^o$
Medium
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Resultant amplitude $=\sqrt{a_{1}^{2}+a_{2}^{2}+2 a_{1} a_{2} \cos \Delta \phi}$
$\Rightarrow \mathrm{a}^{2}=2 \mathrm{a}^{2}+2 \mathrm{a}^{2} \cos \left(\phi_{1}-\phi_{2}\right)$
$\Rightarrow \cos \left(\phi_{1}-\phi_{2}\right)=-\frac{1}{2}$
$\Rightarrow \phi_{1}-\phi_{2}=120^{\circ}$ or $\frac{2 \pi}{3} \mathrm{rad}$
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