Principle of Superposition, Interference and Beats: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Principle of Superposition, Interference and Beats. Understanding the underlying formula is key to arriving at the correct answer below:

For two waves of amplitude \(A\) and phase difference \(phi\), the resultant amplitude is \(A_r = 2A \cos(\frac{\phi}{2})\). Given \(A_r = A\), so \(A = 2A \cos(\frac{\phi}{2})\), which means \(cos(\frac{\phi}{2}) = \frac{1}{2}\). Thus \(\frac{\phi}{2} = 60^\circ\), so \(\phi = 120^\circ\). Hence (A) is true. The resultant amplitude is the sum only if \(\phi = 0\). So (R) is false.