The equations of two waves are given as matrix y₁ = asin (ω t + φ₁)… | MHT CET 2024 (9 May, Shift 2)

Q7MHT CET 2024 · 9 MAY · SHIFT 2Easy

Reflection, Superposition & Interference

The equations of two waves are given as

$\begin{matrix} y_1 = a\sin(\omega t + \phi_1) \\ y_2 = a\sin(\omega t + \phi_2) \end{matrix}$

If amplitude and time period of resultant wave is same as the individual waves, then $(\phi_1 - \phi_2)$ is

Show answer and solution

Answer: (a)

Resultant amplitude: $A_R^2 = a^2 + a^2 + 2a^2\cos\phi$ , with $\phi = \phi_1 - \phi_2$
$A_R = a \Rightarrow a^2 = 2a^2(1 + \cos\phi) \Rightarrow \cos\phi = -\frac{1}{2}$
So the answer is (a) $\cos^{-1}\left(-\frac{1}{2}\right)$ .

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