Three harmonic waves having equal frequency ν and same intensity I₀, have phase angles 0, π/4 and -π/4 respectively. When they are superimposed the intensity of the resultant wave is close to: (a) 5.8 I0 (b) 3 I0 (c) 0.2 I0 (d) I0

Answer: (a). Equal intensities, so equal amplitudes a with I₀ ∝ a². The ±π/4 waves add to 2acos π/4 = √(2)a along the phase-0 wave. AR = a + √(2)a = 2.414a, so I = (2.414)² I₀ ≈ 5.8I₀. So the answer is (a) 5.8I₀.

Three harmonic waves having equal frequency ν and same intensity I₀… | JEE Main 2020 (9 Jan, Shift 1)

Q17JEE Main 2020 · 9 JAN · SHIFT 1Difficult

Reflection, Superposition & Interference

Three harmonic waves having equal frequency $\nu$ and same intensity $I_0$ , have phase angles 0, $\frac{\pi}{4}$ and $-\frac{\pi}{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

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Answer: (a)

Equal intensities, so equal amplitudes $a$ with $I_0 \propto a^2$ .
The $\pm\frac{\pi}{4}$ waves add to $2a\cos\frac{\pi}{4} = \sqrt{2}a$ along the phase-0 wave.
$A_R = a + \sqrt{2}a = 2.414a$ , so $I = (2.414)^2 I_0 \approx 5.8I_0$ .
So the answer is (a) $5.8I_0$ .

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