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If two waves of the same frequency and amplitude respectively on superposition produce a resultant disturbance of the same amplitude, the waves differ in phase by
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Verified Answer
The correct answer is:
$2 \pi / 3$
The resultant amplitude after super position of two wave differing in phase by $\phi$ is given by
$$
\begin{array}{ll}
& A_{R}^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\
\Rightarrow & A_{1}=A_{2}=A_{R}=A \\
\Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi \\
\Rightarrow & \cos \phi=-\frac{1}{2} \\
\Rightarrow & \phi=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}
\end{array}
$$
$$
\begin{array}{ll}
& A_{R}^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\
\Rightarrow & A_{1}=A_{2}=A_{R}=A \\
\Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi \\
\Rightarrow & \cos \phi=-\frac{1}{2} \\
\Rightarrow & \phi=\pi-\frac{\pi}{3}=\frac{2 \pi}{3}
\end{array}
$$
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