The displacement equations of two interfering waves are given by y₁ = 10sin (ω t + π/3) cm, y₂ = 5[sin ω t + √(3)cos ω t] cm respectively. The amplitude of the resultant wave is _______ cm. Numerical answer type. Work it out, then open the answer.

Answer: 20. y₂ = 5sin ω t + 5√(3)cos ω t = 10sin (ω t + π/3) since √(5² + (5√(3))²) = 10 and tan φ = √(3). So y₁ and y₂ are in phase, each of amplitude 10 cm. Resultant amplitude = 10 + 10 = 20 cm.

The displacement equations of two interfering waves are given by y₁ =… | JEE Main 2023 (31 Jan, Shift 2)

Q11JEE Main 2023 · 31 JAN · SHIFT 2Easy

Reflection, Superposition & Interference

The displacement equations of two interfering waves are given by

$y_1 = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ cm}, y_2 = 5[\sin\omega t + \sqrt{3}\cos\omega t]\text{ cm}$ respectively.

The amplitude of the resultant wave is _______ $\text{cm}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 20

$y_2 = 5\sin\omega t + 5\sqrt{3}\cos\omega t = 10\sin\left(\omega t + \frac{\pi}{3}\right)$ since $\sqrt{5^2 + (5\sqrt{3})^2} = 10$ and $\tan\phi = \sqrt{3}$ .
So $y_1$ and $y_2$ are in phase, each of amplitude $10\text{ cm}$ .
Resultant amplitude $= 10 + 10 = 20\text{ cm}$ .

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