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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:
$2 \pi / 3$
Given that, amplitude and frequency of two waves are same.
Hence, resultant amplitude due to superposition of two waves with phase difference $\phi$ is given by
$$
\begin{aligned}
A^{2} &=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\
\Rightarrow A^{2} &=A^{2}+A^{2}+2 A^{2} \cos \phi \\
\Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi
\end{aligned}
$$
$\begin{aligned} \Rightarrow & & \cos \phi &=\frac{-1}{2} \\ \Rightarrow & & \phi &=\frac{2 \pi}{3} \end{aligned}$
Hence, resultant amplitude due to superposition of two waves with phase difference $\phi$ is given by
$$
\begin{aligned}
A^{2} &=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi \\
\Rightarrow A^{2} &=A^{2}+A^{2}+2 A^{2} \cos \phi \\
\Rightarrow & A^{2}=2 A^{2}+2 A^{2} \cos \phi
\end{aligned}
$$
$\begin{aligned} \Rightarrow & & \cos \phi &=\frac{-1}{2} \\ \Rightarrow & & \phi &=\frac{2 \pi}{3} \end{aligned}$
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