Waves and its Characteristics: Practice Problem & Solution
Two waves having equation: $x_1 = a \sin(\omega t + \phi_1)$, $x_2 = a \sin(\omega t + \phi_2)$. If in the resultant wave the frequency and amplitude remains equals to amplitude of superimposing waves. Then phase difference between them: (2001)
Solution Explained:
To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:
Resultant amplitude $A^2 = a^2 + a^2 + 2a^2 \cos(\Delta\phi)$. Given $A = a$, so $a^2 = 2a^2(1 + \cos(\Delta\phi))$. $\cos(\Delta\phi) = -1/2 \Rightarrow \Delta\phi = 2\pi/3$.
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